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.

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.

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.

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.

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.

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.

Network Physiology of Exercise: Vision and Perspectives.

The basic theoretical assumptions of Exercise Physiology and its research directions, strongly influenced by reductionism, may hamper the full potential of basic science investigations, and various practical applications to sports performance and exercise as medicine. The aim of this perspective and programmatic article is to: (i) revise the current paradigm of Exercise Physiology and related research on the basis of principles and empirical findings in the new emerging field of Network Physiology and Complex Systems Science; (ii) initiate a new area in Exercise and Sport Science, Network Physiology of Exercise (NPE), with focus on basic laws of interactions and principles of coordination and integration among diverse physiological systems across spatio-temporal scales (from the sub-cellular level to the entire organism), to understand how physiological states and functions emerge, and to improve the efficacy of exercise in health and sport performance; and (iii) to create a forum for developing new research methodologies applicable to the new NPE field, to infer and quantify nonlinear dynamic forms of coupling among diverse systems and establish basic principles of coordination and network organization of physiological systems. Here, we present a programmatic approach for future research directions and potential practical applications. By focusing on research efforts to improve the knowledge about nested dynamics of vertical network interactions, and particularly, the horizontal integration of key organ systems during exercise, NPE may enrich Basic Physiology and diverse fields like Exercise and Sports Physiology, Sports Medicine, Sports Rehabilitation, Sport Science or Training Science and improve the understanding of diverse exercise-related phenomena such as sports performance, fatigue, overtraining, or sport injuries.

Network Physiology of Cortico-Muscular Interactions.

Skeletal muscle activity is continuously modulated across physiologic states to provide coordination, flexibility and responsiveness to body tasks and external inputs. Despite the central role the muscular system plays in facilitating vital body functions, the network of brain-muscle interactions required to control hundreds of muscles and synchronize their activation in relation to distinct physiologic states has not been investigated. Recent approaches have focused on general associations between individual brain rhythms and muscle activation during movement tasks. However, the specific forms of coupling, the functional network of cortico-muscular coordination, and how network structure and dynamics are modulated by autonomic regulation across physiologic states remains unknown. To identify and quantify the cortico-muscular interaction network and uncover basic features of neuro-autonomic control of muscle function, we investigate the coupling between synchronous bursts in cortical rhythms and peripheral muscle activation during sleep and wake. Utilizing the concept of time delay stability and a novel network physiology approach, we find that the brain-muscle network exhibits complex dynamic patterns of communication involving multiple brain rhythms across cortical locations and different electromyographic frequency bands. Moreover, our results show that during each physiologic state the cortico-muscular network is characterized by a specific profile of network links strength, where particular brain rhythms play role of main mediators of interaction and control. Further, we discover a hierarchical reorganization in network structure across physiologic states, with high connectivity and network link strength during wake, intermediate during REM and light sleep, and low during deep sleep, a sleep-stage stratification that demonstrates a unique association between physiologic states and cortico-muscular network structure. The reported empirical observations are consistent across individual subjects, indicating universal behavior in network structure and dynamics, and high sensitivity of cortico-muscular control to changes in autonomic regulation, even at low levels of physical activity and muscle tone during sleep. Our findings demonstrate previously unrecognized basic principles of brain-muscle network communication and control, and provide new perspectives on the regulatory mechanisms of brain dynamics and locomotor activation, with potential clinical implications for neurodegenerative, movement and sleep disorders, and for developing efficient treatment strategies.

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.

Universal spectral profile and dynamic evolution of muscle activation: a hallmark of muscle type and physiological state.

The skeletal muscle is an integrated multicomponent system with complex dynamics of continuous myoelectrical activation of various muscle types across time scales to facilitate muscle coordination among units and adaptation to physiological states. To understand the multiscale dynamics of neuromuscular activity, we investigated spectral characteristics of different muscle types across time scales and their evolution with physiological states. We hypothesized that each muscle type is characterized by a specific spectral profile, reflecting muscle composition and function, that remains invariant over time scales and is universal across subjects. Furthermore, we hypothesized that the myoelectrical activation and corresponding spectral profile during certain movements exhibit an evolution path in time that is unique for each muscle type and reflects responses in muscle dynamics to exercise, fatigue, and aging. To probe the multiscale mechanism of neuromuscular regulation, we developed a novel protocol of repeated squat exercise segments, each performed until exhaustion, and we analyzed differentiated spectral power responses over a range of frequency bands for leg and back muscle activation in young and old subjects. We found that leg and back muscle activation is characterized by muscle-specific spectral profiles, with differentiated frequency band contribution, and a muscle-specific evolution path in response to fatigue and aging that is universal across subjects in each age group. The uncovered universality among subjects in the spectral profile of each muscle at a given physiological state, as well as the robustness in the evolution of these profiles over a range of time scales and states, reveals a previously unrecognized multiscale mechanism underlying the differentiated response of distinct muscle types to exercise-induced fatigue and aging.NEW & NOTEWORTHY To understand coordinated function of distinct fibers in a muscle, we investigated spectral dynamics of muscle activation during maximal exercise across a range of frequency bands and time scales of observation. We discovered a spectral profile that is specific for each muscle type, robust at short, intermediate, and large time scales, universal across subjects, and characterized by a muscle-specific evolution path with accumulation of fatigue and aging, indicating a previously unrecognized multiscale mechanism of muscle tone regulation.

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.

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.

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

Brain rhythms are associated with a range of physiologic states, and thus, studies have traditionally focused on neuronal origin, temporal dynamics and fundamental role of individual brain rhythms, and more recently on specific pair-wise interactions. Here, we aim to understand integrated physiologic function as an emergent phenomenon of dynamic network interactions among brain rhythms. We hypothesize that brain rhythms continuously coordinate their activations to facilitate physiologic states and functions. We analyze healthy subjects during sleep, and we demonstrate the presence of stable interaction patterns among brain rhythms. Probing transient modulations in brain wave activation, we discover three classes of interaction patterns that form an ensemble representative for each sleep stage, indicating an association of each state with a specific network of brain-rhythm communications. The observations are universal across subjects and identify networks of brain-rhythm interactions as a hallmark of physiologic state and function, providing new insights on neurophysiological regulation with broad clinical implications.