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

Jilin W J L Wang,Plamen Ch Ivanov,Fabrizio Lombardi,Christelle Anaclet,Xiyun Zhang,Bard Ermentrout

doi:10.1371/journal.pcbi.1007268

Abstract

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.

Highlights

The brain’s ability to adapt and perform complex functions crucially depends on the cooperation of assemblies of neurons across multiple spatial and temporal scales
We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range powerlaw correlations and a robust duality of power law (θ-bursts, active phase) and exponentiallike (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality
In each window, the spectral power is primarily concentrated in either the δ-wave frequency range (0 − 4Hz) or in the θwave band (4 − 8Hz), and we observe sharp transitions from periods with dominant δ to periods with dominant θ waves. Such dynamics can be understood as the temporal evolution of the ratio Rθδ = S(θ)/S(δ) between θ and δ spectral power in association with different physiological states—NREM, REM and arousals/wake (Fig 1 shows the transient dynamics of bursts in δ- and θ-waves power represented by the logarithm of Rθδ as a function of time t)

Summary

Introduction

The brain’s ability to adapt and perform complex functions crucially depends on the cooperation of assemblies of neurons across multiple spatial and temporal scales. Cortical rhythms represent one of the most fascinating collective phenomena emerging from the self-organized synchronous activity of large neuronal populations, and are consistently associated with complex brain functions and distinct physiologic states such as sleep and wake [1, 2]. During deep NREM sleep, brain dynamics are generally dominated by δ rhythm, low-frequency high-amplitude oscillations referred to as slow-wave activity [3]. Such slow-wave oscillations result from the synchronized activity of cortical neurons alternating between ‘up’ and ‘down’ states. In contrast to NREM sleep, REM sleep and arousals/wake state are characterized by desychronized and localized cortical rhythms of higher frequency and lower amplitude, such as α waves in resting humans and θ waves in rodents [9]. During REM sleep, hippocampal θ rhythm is driven by GABAergic inputs from the medial septum [11]

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