Role of the Locus Coeruleus Arousal Promoting Neurons in Maintaining Brain Criticality across the Sleep-Wake Cycle.

Sleep control depends on a delicate interplay among brain regions. This generates a complex temporal architecture with numerous sleep-stage transitions and intermittent fluctuations to micro-states and brief arousals. These temporal dynamics exhibit hallmarks of criticality, suggesting that tuning to criticality is essential for spontaneous sleep-stage and arousal transitions. However, how the brain maintains criticality remains not understood. Here, we investigate θ- and δ-burst dynamics during the sleep-wake cycle of rats (Sprague-Dawley, adult male) with lesion in the wake-promoting locus coeruleus (LC). We show that, in control rats, θ- and δ-bursts exhibit power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, as well as power-law long-range temporal correlations (LRTCs)-typical of non-equilibrium systems self-organizing at criticality. Furthermore, consecutive θ- and δ-bursts durations are characterized by anti-correlated coupling, indicating a new class of self-organized criticality that emerges from underlying feedback between neuronal populations and brain areas involved in generating arousals and sleep states. In contrast, we uncover that LC lesion leads to alteration of θ- and δ-burst critical features, with change in duration distributions and correlation properties, and increase in θ-δ coupling. Notably, these LC-lesion effects are opposite to those observed for lesions in the sleep-promoting ventrolateral preoptic (VLPO) nucleus. Our findings indicate that critical dynamics of θ- and δ-bursts arise from a balanced interplay of LC and VLPO, which maintains brain tuning to criticality across the sleep-wake cycle-a non-equilibrium behavior in sleep micro-architecture at short timescales that coexists with large-scale sleep-wake homeostasis.

Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake.

Origin and functions of intermittent transitions among sleep stages, including brief awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing sleep on scales of seconds and minutes results from intrinsic non-equilibrium critical dynamics. We investigate θ- and δ-wave dynamics in control rats and in rats where the sleep-promoting ventrolateral preoptic nucleus (VLPO) is lesioned (male Sprague-Dawley rats). We demonstrate that bursts in θ and δ cortical rhythms exhibit complex temporal organization, with long-range correlations and robust duality of power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, features typical of non-equilibrium systems self-organizing at criticality. We show that such non-equilibrium behavior relates to anti-correlated coupling between θ- and δ-bursts, persists across a range of time scales, and is independent of the dominant physiologic state; indications of a basic principle in sleep regulation. Further, we find that VLPO lesions lead to a modulation of cortical dynamics resulting in altered dynamical parameters of θ- and δ-bursts and significant reduction in θ-δ coupling. Our empirical findings and model simulations demonstrate that θ-δ coupling is essential for the emerging non-equilibrium critical dynamics observed across the sleep-wake cycle, and indicate that VLPO neurons may have dual role for both sleep and arousal/brief wake activation. The uncovered critical behavior in sleep- and wake-related cortical rhythms indicates a mechanism essential for the micro-architecture of spontaneous sleep-stage and arousal transitions within a novel, non-homeostatic paradigm of sleep regulation.SIGNIFICANCE STATEMENT We show that the complex micro-architecture of sleep-stage/arousal transitions arises from intrinsic non-equilibrium critical dynamics, connecting the temporal organization of dominant cortical rhythms with empirical observations across scales. We link such behavior to sleep-promoting neuronal population, and demonstrate that VLPO lesion (model of insomnia) alters dynamical features of θ and δ rhythms, and leads to significant reduction in θ-δ coupling. This indicates that VLPO neurons may have dual role for both sleep and arousal/brief wake control. The reported empirical findings and modeling simulations constitute first evidences of a neurophysiological fingerprint of self-organization and criticality in sleep- and wake-related cortical rhythms; a mechanism essential for spontaneous sleep-stage and arousal transitions that lays the bases for a novel, non-homeostatic paradigm of sleep regulation.

Quantifying financial market dynamics: Scaling law in rank mobility of Chinese stock prices.

Rank mobility, which was designed to measure the average variation of relative rank positions with respect to any absolute variable over a given time period, can be used to explore how the memory of stock price ranking orders fades over time. We investigate the variation in rank order of the closing prices of stocks registered at the Shanghai A-share market over a long period of 16 years. And we find that rank mobility increases as a power law with increasing time scale, and eventually converges to a constant level. This power-law relationship can be observed not only over a long period of 16 years but also for each consecutive year, especially their power law exponents are very close. The empirical evidence indicates a fundamental dynamics of Chinese stock price movements.

ß Cells Operate Collectively to Help Maintain Glucose Homeostasis.

Residing in the islets of Langerhans in the pancreas, ß cells contribute to glucose homeostasis by managing the body's insulin supply. Although it has been acknowledged that healthy ß cells engage in heavy cell-to-cell communication to perform their homeostatic function, the exact role and effects of such communication remain partly understood. We offer a novel, to our knowledge, perspective on the subject in the form of 1) a dynamical network model that faithfully mimics fast calcium oscillations in response to above-threshold glucose stimulation and 2) empirical data analysis that reveals a qualitative shift in the cross-correlation structure of measured signals below and above the threshold glucose concentration. Combined together, these results point to a glucose-induced transition in ß-cell activity thanks to increasing coordination through gap-junctional signaling and paracrine interactions. Our data and the model further suggest how the conservation of entire cell-cell conductance, observed in coupled but not uncoupled ß cells, emerges as a collective phenomenon. An overall implication is that improving the ability to monitor ß-cell signaling should offer means to better understand the pathogenesis of diabetes mellitus.

Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture.

Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.

Focus on the emerging new fields of Network Physiology and Network Medicine.

Despite the vast progress and achievements in systems biology and integrative physiology in the last decades, there is still a significant gap in understanding the mechanisms through which (i) genomic, proteomic and metabolic factors and signaling pathways impact vertical processes across cells, tissues and organs leading to the expression of different disease phenotypes and influence the functional and clinical associations between diseases, and (ii) how diverse physiological systems and organs coordinate their functions over a broad range of space and time scales and horizontally integrate to generate distinct physiologic states at the organism level. Two emerging fields, network medicine and network physiology, aim to address these fundamental questions. Novel concepts and approaches derived from recent advances in network theory, coupled dynamical systems, statistical and computational physics show promise to provide new insights into the complexity of physiological structure and function in health and disease, bridging the genetic and sub-cellular level with inter-cellular interactions and communications among integrated organ systems and sub-systems. These advances form first building blocks in the methodological formalism and theoretical framework necessary to address fundamental problems and challenges in physiology and medicine. This 'focus on' issue contains 26 articles representing state-of-the-art contributions covering diverse systems from the sub-cellular to the organism level where physicists have key role in laying the foundations of these new fields.

Phase transitions in physiologic coupling.

Integrated physiological systems, such as the cardiac and the respiratory system, exhibit complex dynamics that are further influenced by intrinsic feedback mechanisms controlling their interaction. To probe how the cardiac and the respiratory system adjust their rhythms, despite continuous fluctuations in their dynamics, we study the phase synchronization of heartbeat intervals and respiratory cycles. The nature of this interaction, its physiological and clinical relevance, and its relation to mechanisms of neural control is not well understood. We investigate whether and how cardiorespiratory phase synchronization (CRPS) responds to changes in physiological states and conditions. We find that the degree of CRPS in healthy subjects dramatically changes with sleep-stage transitions and exhibits a pronounced stratification pattern with a 400% increase from rapid eye movement sleep and wake, to light and deep sleep, indicating that sympatho-vagal balance strongly influences CRPS. For elderly subjects, we find that the overall degree of CRPS is reduced by approximately 40%, which has important clinical implications. However, the sleep-stage stratification pattern we uncover in CRPS does not break down with advanced age, and surprisingly, remains stable across subjects. Our results show that the difference in CRPS between sleep stages exceeds the difference between young and elderly, suggesting that sleep regulation has a significantly stronger effect on cardiorespiratory coupling than healthy aging. We demonstrate that CRPS and the traditionally studied respiratory sinus arrhythmia represent different aspects of the cardiorespiratory interaction, and that key physiologic variables, related to regulatory mechanisms of the cardiac and respiratory systems, which influence respiratory sinus arrhythmia, do not affect CRPS.

Major component analysis of dynamic networks of physiologic organ interactions.

The human organism is a complex network of interconnected organ systems, where the behavior of one system affects the dynamics of other systems. Identifying and quantifying dynamical networks of diverse physiologic systems under varied conditions is a challenge due to the complexity in the output dynamics of the individual systems and the transient and non-linear characteristics of their coupling. We introduce a novel computational method based on the concept of time delay stability and major component analysis to investigate how organ systems interact as a network to coordinate their functions. We analyze a large database of continuously recorded multi-channel physiologic signals from healthy young subjects during night-time sleep. We identify a network of dynamic interactions between key physiologic systems in the human organism. Further, we find that each physiologic state is characterized by a distinct network structure with different relative contribution from individual organ systems to the global network dynamics. Specifically, we observe a gradual decrease in the strength of coupling of heart and respiration to the rest of the network with transition from wake to deep sleep, and in contrast, an increased relative contribution to network dynamics from chin and leg muscle tone and eye movement, demonstrating a robust association between network topology and physiologic function.

Network of muscle fibers activation facilitates inter-muscular coordination, adapts to fatigue and reflects muscle function.

Fundamental movement patterns require continuous skeletal muscle coordination, where muscle fibers with different timing of activation synchronize their dynamics across muscles with distinct functions. It is unknown how muscle fibers integrate as a network to generate and fine tune movements. We investigate how distinct muscle fiber types synchronize across arm and chest muscles, and respond to fatigue during maximal push-up exercise. We uncover that a complex inter-muscular network of muscle fiber cross-frequency interactions underlies push-up movements. The network exhibits hierarchical organization (sub-networks/modules) with specific links strength stratification profile, reflecting distinct functions of muscles involved in push-up movements. We find network reorganization with fatigue where network modules follow distinct phase-space trajectories reflecting their functional role and adaptation to fatigue. Consistent with earlier observations for squat movements under same protocol, our findings point to general principles of inter-muscular coordination for fundamental movements, and open a new area of research, Network Physiology of Exercise.

Dynamic networks of cortico-muscular interactions in sleep and neurodegenerative disorders.

The brain plays central role in regulating physiological systems, including the skeleto-muscular and locomotor system. Studies of cortico-muscular coordination have primarily focused on associations between movement tasks and dynamics of specific brain waves. However, the brain-muscle functional networks of synchronous coordination among brain waves and muscle activity rhythms that underlie locomotor control remain unknown. Here we address the following fundamental questions: what are the structure and dynamics of cortico-muscular networks; whether specific brain waves are main network mediators in locomotor control; how the hierarchical network organization relates to distinct physiological states under autonomic regulation such as wake, sleep, sleep stages; and how network dynamics are altered with neurodegenerative disorders. We study the interactions between all physiologically relevant brain waves across cortical locations with distinct rhythms in leg and chin muscle activity in healthy and Parkinson's disease (PD) subjects. Utilizing Network Physiology framework and time delay stability approach, we find that 1) each physiological state is characterized by a unique network of cortico-muscular interactions with specific hierarchical organization and profile of links strength; 2) particular brain waves play role as main mediators in cortico-muscular interactions during each state; 3) PD leads to muscle-specific breakdown of cortico-muscular networks, altering the sleep-stage stratification pattern in network connectivity and links strength. In healthy subjects cortico-muscular networks exhibit a pronounced stratification with stronger links during wake and light sleep, and weaker links during REM and deep sleep. In contrast, network interactions reorganize in PD with decline in connectivity and links strength during wake and non-REM sleep, and increase during REM, leading to markedly different stratification with gradual decline in network links strength from wake to REM, light and deep sleep. Further, we find that wake and sleep stages are characterized by specific links strength profiles, which are altered with PD, indicating disruption in the synchronous activity and network communication among brain waves and muscle rhythms. Our findings demonstrate the presence of previously unrecognized functional networks and basic principles of brain control of locomotion, with potential clinical implications for novel network-based biomarkers for early detection of Parkinson's and neurodegenerative disorders, movement, and sleep disorders.

Inter-muscular networks of synchronous muscle fiber activation.

Skeletal muscles continuously coordinate to facilitate a wide range of movements. Muscle fiber composition and timing of activation account for distinct muscle functions and dynamics necessary to fine tune muscle coordination and generate movements. Here we address the fundamental question of how distinct muscle fiber types dynamically synchronize and integrate as a network across muscles with different functions. We uncover that physiological states are characterized by unique inter-muscular network of muscle fiber cross-frequency interactions with hierarchical organization of distinct sub-networks and modules, and a stratification profile of links strength specific for each state. We establish how this network reorganizes with transition from rest to exercise and fatigue-a complex process where network modules follow distinct phase-space trajectories reflecting their functional role in movements and adaptation to fatigue. This opens a new area of research, Network Physiology of Exercise, leading to novel network-based biomarkers of health, fitness and clinical conditions.

Dynamic networks of physiologic interactions of brain waves and rhythms in muscle activity.

The brain plays a central role in facilitating vital body functions and in regulating physiological and organ systems, including the skeleto-muscular and locomotor system. While neural control is essential to synchronize and coordinate activation of various muscle groups and muscle fibers within muscle groups in relation to body movements and distinct physiologic states, the dynamic networks of brain-muscle interactions have not been explored and the complex regulatory mechanism of brain-muscle control remains unknown. Here we present a first study of network interactions between brain waves at different cortical locations and peripheral muscle activity across key physiologic states - wake, sleep and distinct sleep stages. Utilizing a novel approach based on the Network Physiology framework and the concept of time delay stability, we find that for each physiologic state the network of cortico-muscular interactions is characterized by a specific hierarchical organization of network topology and network links strength, where particular brain waves are main mediators of interaction and control of muscular activity. Further, we uncover that with transition from one physiological state to another, the brain-muscle interaction network undergoes marked reorganization in the profile of network links strength, indicating a direct association between network structure and physiological state and function. The pronounced stratification in brain-muscle network characteristics across sleep stages is consistent for chin and leg muscle groups and persists across subjects, indicating a remarkable universality and a previously unrecognized basic physiologic mechanism that regulates muscle activity even during rest and in the absence targeted direct movement. Our findings demonstrate previously unrecognized coordination between brain waves and activation of different muscle fiber types within muscle groups, laws of brain-muscle cross-communication and principles of network integration and control. These investigations demonstrate the potential of network-based biomarkers for classification of distinct physiological states and conditions, for the diagnosis and prognosis of neurodegenerative, movement and sleep disorders, and for developing efficient treatment strategies.

Ensemble of coupling forms and networks among brain rhythms as function of states and cognition.

The current paradigm in brain research focuses on individual brain rhythms, their spatiotemporal organization, and specific pairwise interactions in association with physiological states, cognitive functions, and pathological conditions. Here we propose a conceptually different approach to understanding physiologic function as emerging behavior from communications among distinct brain rhythms. We hypothesize that all brain rhythms coordinate as a network to generate states and facilitate functions. We analyze healthy subjects during rest, exercise, and cognitive tasks and show that synchronous modulation in the micro-architecture of brain rhythms mediates their cross-communications. We discover that brain rhythms interact through an ensemble of coupling forms, universally observed across cortical areas, uniquely defining each physiological state. We demonstrate that a dynamic network regulates the collective behavior of brain rhythms and that network topology and links strength hierarchically reorganize with transitions across states, indicating that brain-rhythm interactions play an essential role in generating physiological states and cognition.

Network Physiology of Exercise: Beyond Molecular and Omics Perspectives.

Molecular Exercise Physiology and Omics approaches represent an important step toward synthesis and integration, the original essence of Physiology. Despite the significant progress they have introduced in Exercise Physiology (EP), some of their theoretical and methodological assumptions are still limiting the understanding of the complexity of sport-related phenomena. Based on general principles of biological evolution and supported by complex network science, this paper aims to contrast theoretical and methodological aspects of molecular and network-based approaches to EP. After explaining the main EP challenges and why sport-related phenomena cannot be understood if reduced to the molecular level, the paper proposes some methodological research advances related to the type of studied variables and measures, the data acquisition techniques, the type of data analysis and the assumed relations among physiological levels. Inspired by Network Physiology, Network Physiology of Exercise provides a new paradigm and formalism to quantify cross-communication among diverse systems across levels and time scales to improve our understanding of exercise-related phenomena and opens new horizons for exercise testing in health and disease.

Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals.

We investigate how various coarse-graining (signal quantization) methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the magnitude of a signal, we consider (i) the Floor, (ii) the Symmetry and (iii) the Centro-Symmetry coarse-graining methods. We find that for anti-correlated signals coarse-graining in the magnitude leads to a crossover to random behavior at large scales, and that with increasing the width of the coarse-graining partition interval Δ, this crossover moves to intermediate and small scales. In contrast, the scaling of positively correlated signals is less affected by the coarse-graining, with no observable changes when Δ < 1, while for Δ > 1 a crossover appears at small scales and moves to intermediate and large scales with increasing Δ. For very rough coarse-graining (Δ > 3) based on the Floor and Symmetry methods, the position of the crossover stabilizes, in contrast to the Centro-Symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales; thus indicating a much stronger effect of the Centro-Symmetry compared to the Floor and the Symmetry method. For coarse-graining in time, where data points are averaged in non-overlapping time windows, we find that the scaling for both anti-correlated and positively correlated signals is practically preserved. The results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences.

Aging effects on cardiac and respiratory dynamics in healthy subjects across sleep stages.

STUDY OBJECTIVES: Respiratory and heart rate variability exhibit fractal scaling behavior on certain time scales. We studied the short-term and long-term correlation properties of heartbeat and breathing-interval data from disease-free subjects focusing on the age-dependent fractal organization. We also studied differences across sleep stages and night-time wake and investigated quasi-periodic variations associated with cardiac risk. DESIGN: Full-night polysomnograms were recorded during 2 nights, including electrocardiogram and oronasal airflow. SETTING: Data were collected in 7 laboratories in 5 European countries. PARTICIPANTS: 180 subjects without health complaints (85 males, 95 females) aged from 20 to 89 years. INTERVENTIONS: None. MEASUREMENTS AND RESULTS: Short-term correlations in heartbeat intervals measured by the detrended fluctuation analysis (DFA) exponent alpha1 show characteristic age dependence with a maximum around 50-60 years disregarding the dependence on sleep and wake states. Long-term correlations measured by alpha2 differ in NREM sleep when compared with REM sleep and wake, besides weak age dependence. Results for respiratory intervals are similar to those for alpha2 of heartbeat intervals. Deceleration capacity (DC) decreases with age; it is lower during REM and deep sleep (compared with light sleep and wake). CONCLUSION: The age dependence of alpha1 should be considered when using this value for diagnostic purposes in post-infarction patients. Pronounced long-term correlations (larger alpha2) for heartbeat and respiration during REM sleep and wake indicate an enhanced control of higher brain regions, which is absent during NREM sleep. Reduced DC possibly indicates an increased cardiovascular risk with aging and during REM and deep sleep.

Endogenous circadian rhythm in human motor activity uncoupled from circadian influences on cardiac dynamics.

The endogenous circadian pacemaker influences key physiologic functions, such as body temperature and heart rate, and is normally synchronized with the sleep/wake cycle. Epidemiological studies demonstrate a 24-h pattern in adverse cardiovascular events with a peak at approximately 10 a.m. It is unknown whether this pattern in cardiac risk is caused by a day/night pattern of behaviors, including activity level and/or influences from the internal circadian pacemaker. We recently found that a scaling index of cardiac vulnerability has an endogenous circadian peak at the circadian phase corresponding to approximately 10 a.m., which conceivably could contribute to the morning peak in cardiac risk. Here, we test whether this endogenous circadian influence on cardiac dynamics is caused by circadian-mediated changes in motor activity or whether activity and heart rate dynamics are decoupled across the circadian cycle. We analyze high-frequency recordings of motion from young healthy subjects during two complementary protocols that decouple the sleep/wake cycle from the circadian cycle while controlling scheduled behaviors. We find that static activity properties (mean and standard deviation) exhibit significant circadian rhythms with a peak at the circadian phase corresponding to 5-9 p.m. ( approximately 9 h later than the peak in the scale-invariant index of heartbeat fluctuations). In contrast, dynamic characteristics of the temporal scale-invariant organization of activity fluctuations (long-range correlations) do not exhibit a circadian rhythm. These findings suggest that endogenous circadian-mediated activity variations are not responsible for the endogenous circadian rhythm in the scale-invariant structure of heartbeat fluctuations and likely do not contribute to the increase in cardiac risk at approximately 10 a.m.

Power-law correlations and coupling of active and quiet states underlie a class of complex systems with self-organization at criticality.

Physical and biological systems often exhibit intermittent dynamics with bursts or avalanches (active states) characterized by power-law size and duration distributions. These emergent features are typical of systems at the critical point of continuous phase transitions, and have led to the hypothesis that such systems may self-organize at criticality, i.e. without any fine tuning of parameters. Since the introduction of the Bak-Tang-Wiesenfeld (BTW) model, the paradigm of self-organized criticality (SOC) has been very fruitful for the analysis of emergent collective behaviors in a number of systems, including the brain. Although considerable effort has been devoted in identifying and modeling scaling features of burst and avalanche statistics, dynamical aspects related to the temporal organization of bursts remain often poorly understood or controversial. Of crucial importance to understand the mechanisms responsible for emergent behaviors is the relationship between active and quiet periods, and the nature of the correlations. Here we investigate the dynamics of active (θ-bursts) and quiet states (δ-bursts) in brain activity during the sleep-wake cycle. We show the duality of power-law (θ, active phase) and exponential-like (δ, quiescent phase) duration distributions, typical of SOC, jointly emerge with power-law temporal correlations and anti-correlated coupling between active and quiet states. Importantly, we demonstrate that such temporal organization shares important similarities with earthquake dynamics, and propose that specific power-law correlations and coupling between active and quiet states are distinctive characteristics of a class of systems with self-organization at criticality.

Author Correction: Dynamic network interactions among distinct brain rhythms as a hallmark of physiologic state and function.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.