Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons

We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or `short-cuts' and the delay in the neuronal interactions. Persistent activity arises for a small fraction of `short-cuts', while a transition to failure occurs at a critical value of the `short-cut' density. The persistent activity consists of multi-stable periodic attractors, the number of which is at least on the order of the number of neurons in the network. For long enough delays, network activity at high `short-cut' densities is shown to exhibit exceedingly long chaotic transients whose failure-times averaged over many network configurations follow a stretched exponential. We show how this functional form arises in the ensemble-averaged activity if each network realization has a characteristic failure-time which is exponentially distributed.Comment: 14 pages 23 figure

The brain decade in debate: VII. Neurobiology of sleep and dreams

This article is a transcription of an electronic symposium held on February 5, 2001 by the Brazilian Society of Neuroscience and Behavior (SBNeC) during which eight specialists involved in clinical and experimental research on sleep and dreaming exposed their personal experience and theoretical points of view concerning these highly polemic subjects. Unlike most other bodily functions, sleep and dreaming cannot, so far, be defined in terms of definitive functions that play an ascribable role in maintaining the organism as a whole. Such difficulties appear quite clearly all along the discussions. In this symposium, concepts on sleep function range from a protective behavior to an essential function for maturation of the nervous system. Kleitman's hypothesis [Journal of Nervous and Mental Disease (1974), 159: 293-294] was discussed, according to which the basal state is not the wakeful state but sleep, from which we awake to eat, to protect ourselves, to procreate, etc. Dreams, on the other hand, were widely discussed, being considered either as an important step in consolidation of learning or simply the conscious identification of functional patterns derived from the configuration of released or revoked memorized information.Universidade de São Paulo Faculdade de Medicina Instituto de PsiquiatriaUniversity of Laval School of Medicine Department of PhysiologyRutgers State University Center for NeuroscienceUniversidade de São Paulo Instituto de Ciências Biomédicas Departamento de Fisiologia e BiofísicaUniversidade Federal de São Paulo (UNIFESP) Instituto do SonhoFacultad de Medicina de Montevideo Departamento de Fisiología NeurofisiologíaFlorida Atlantic University Center for Complex SystemsUniversidade de São Paulo Faculdade de Medicina Departamento de NeurologiaUNIFESP, Instituto do SonhoSciEL

Robust Off- and Online Separation of Intracellularly Recorded Up and Down Cortical States

BACKGROUND: The neuronal cortical network generates slow (<1 Hz) spontaneous rhythmic activity that emerges from the recurrent connectivity. This activity occurs during slow wave sleep or anesthesia and also in cortical slices, consisting of alternating up (active, depolarized) and down (silent, hyperpolarized) states. The search for the underlying mechanisms and the possibility of analyzing network dynamics in vitro has been subject of numerous studies. This exposes the need for a detailed quantitative analysis of the membrane fluctuating behavior and computerized tools to automatically characterize the occurrence of up and down states. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular recordings from different areas of the cerebral cortex were obtained from both in vitro and in vivo preparations during slow oscillations. A method that separates up and down states recorded intracellularly is defined and analyzed here. The method exploits the crossover of moving averages, such that transitions between up and down membrane regimes can be anticipated based on recent and past voltage dynamics. We demonstrate experimentally the utility and performance of this method both offline and online, the online use allowing to trigger stimulation or other events in the desired period of the rhythm. This technique is compared with a histogram-based approach that separates the states by establishing one or two discriminating membrane potential levels. The robustness of the method presented here is tested on data that departs from highly regular alternating up and down states. CONCLUSIONS/SIGNIFICANCE: We define a simple method to detect cortical states that can be applied in real time for offline processing of large amounts of recorded data on conventional computers. Also, the online detection of up and down states will facilitate the study of cortical dynamics. An open-source MATLAB toolbox, and Spike 2-compatible version are made freely available

Large-Scale Cortical Dynamics of Sleep Slow Waves

Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions

Cortical Layer 1 and Layer 2/3 Astrocytes Exhibit Distinct Calcium Dynamics In Vivo

Cumulative evidence supports bidirectional interactions between astrocytes and neurons, suggesting glial involvement of neuronal information processing in the brain. Cytosolic calcium (Ca2+) concentration is important for astrocytes as Ca2+ surges co-occur with gliotransmission and neurotransmitter reception. Cerebral cortex is organized in layers which are characterized by distinct cytoarchitecture. We asked if astrocyte-dominant layer 1 (L1) of the somatosensory cortex was different from layer 2/3 (L2/3) in spontaneous astrocytic Ca2+ activity and if it was influenced by background neural activity. Using a two-photon laser scanning microscope, we compared spontaneous Ca2+ activity of astrocytic somata and processes in L1 and L2/3 of anesthetized mature rat somatosensory cortex. We also assessed the contribution of background neural activity to the spontaneous astrocytic Ca2+ dynamics by investigating two distinct EEG states (“synchronized” vs. “de-synchronized” states). We found that astrocytes in L1 had nearly twice higher Ca2+ activity than L2/3. Furthermore, Ca2+ fluctuations of processes within an astrocyte were independent in L1 while those in L2/3 were synchronous. Pharmacological blockades of metabotropic receptors for glutamate, ATP, and acetylcholine, as well as suppression of action potentials did not have a significant effect on the spontaneous somatic Ca2+ activity. These results suggest that spontaneous astrocytic Ca2+ surges occurred in large part intrinsically, rather than neural activity-driven. Our findings propose a new functional segregation of layer 1 and 2/3 that is defined by autonomous astrocytic activity

Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep

Effect of crystalline disorder on quantum tunneling in the single-molecule magnet Mn12 benzoate

10 páginas, 9 figuras, 1 tabla.-- PACS number(s): 75.45.+j, 75.50.Xx, 75.60.Jk, 75.50.Kj.-- et al.We report a detailed study of the effects that crystalline disorder has on the magnetic relaxation and quantum tunneling of Mn12 benzoate clusters. Thanks to the absence of interstitial molecules in the crystal structure of this molecular compound, we have been able to isolate the influence of long-range crystalline disorder. For this, we compare results obtained under two extreme situations: a crystalline sample and a nearly amorphous material. The results show that crystalline disorder affects little the anisotropy, magnetic relaxation, and quantum tunneling of these materials. It follows that disorder is not a necessary ingredient for the existence of magnetic quantum tunneling. The results unveil, however, a subtle influence of crystallinity via the modification of the symmetry of dipole-dipole interactions. The faster tunneling rates measured for the amorphous material are accounted for by a narrower distribution of dipolar bias in this material, as compared with the crystalline sample.This work has been partly funded by Grants No. MAT2009-13977-C03, No. MAT2008-06542- C04, and No. CSD2007-00010 from the Spanish Ministerio de Ciencia e Innovación, and NABISUP from DGA. We acknowledge funding from Acción Integrada under Grant No. HA2006-0051 and the Network of Excellence MAGMANet. J.v.S and S.D. acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) and the DAAD. Ch.C. and I.I. acknowledge the Spanish Ministerio de Ciencia e Innovación.Peer reviewe

Acoustic Oddball during NREM Sleep: A Combined EEG/fMRI Study

Background: A condition vital for the consolidation and maintenance of sleep is generally reduced responsiveness to external stimuli. Despite this, the sleeper maintains a level of stimulus processing that allows to respond to potentially dangerous environmental signals. The mechanisms that subserve these contradictory functions are only incompletely understood. Methodology/Principal Findings: Using combined EEG/fMRI we investigated the neural substrate of sleep protection by applying an acoustic oddball paradigm during light NREM sleep. Further, we studied the role of evoked K-complexes (KCs), an electroencephalographic hallmark of NREM sleep with a still unknown role for sleep protection. Our main results were: (1) Other than in wakefulness, rare tones did not induce a blood oxygenation level dependent (BOLD) signal increase in the auditory pathway but a strong negative BOLD response in motor areas and the amygdala. (2) Stratification of rare tones by the presence of evoked KCs detected activation of the auditory cortex, hippocampus, superior and middle frontal gyri and posterior cingulate only for rare tones followed by a KC. (3) The typical high frontocentral EEG deflections of KCs were not paralleled by a BOLD equivalent. Conclusions/Significance: We observed that rare tones lead to transient disengagement of motor and amygdala responses during light NREM sleep. We interpret this as a sleep protective mechanism to delimit motor responses and to reduce the sensitivity of the amygdala towards further incoming stimuli. Evoked KCs are suggested to originate from a brain state wit

Morning and Evening-Type Differences in Slow Waves during NREM Sleep Reveal Both Trait and State-Dependent Phenotypes

Brain recovery after prolonged wakefulness is characterized by increased density, amplitude and slope of slow waves (SW, <4 Hz) during non-rapid eye movement (NREM) sleep. These SW comprise a negative phase, during which cortical neurons are mostly silent, and a positive phase, in which most neurons fire intensively. Previous work showed, using EEG spectral analysis as an index of cortical synchrony, that Morning-types (M-types) present faster dynamics of sleep pressure than Evening-types (E-types). We thus hypothesized that single SW properties will also show larger changes in M-types than in E-types in response to increased sleep pressure. SW density (number per minute) and characteristics (amplitude, slope between negative and positive peaks, frequency and duration of negative and positive phases) were compared between chronotypes for a baseline sleep episode (BL) and for recovery sleep (REC) after two nights of sleep fragmentation. While SW density did not differ between chronotypes, M-types showed higher SW amplitude and steeper slope than E-types, especially during REC. SW properties were also averaged for 3 NREM sleep periods selected for their decreasing level of sleep pressure (first cycle of REC [REC1], first cycle of BL [BL1] and fourth cycle of BL [BL4]). Slope was significantly steeper in M-types than in E-types in REC1 and BL1. SW frequency was consistently higher and duration of positive and negative phases constantly shorter in M-types than in E-types. Our data reveal that specific properties of cortical synchrony during sleep differ between M-types and E-types, although chronotypes show a similar capacity to generate SW. These differences may involve 1) stable trait characteristics independent of sleep pressure (i.e., frequency and durations) likely linked to the length of silent and burst-firing phases of individual neurons, and 2) specific responses to increased sleep pressure (i.e., slope and amplitude) expected to depend on the synchrony between neurons