Phase-Coherence Transitions and Communication in the Gamma Range between Delay-Coupled Neuronal Populations

Synchronization between neuronal populations plays an important role in information transmission between brain areas. In particular, collective oscillations emerging from the synchronized activity of thousands of neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony of neuronal activity can take place within a cortical patch or between different cortical regions. While short-range interactions between neurons involve just a few milliseconds, communication through long-range projections between different regions could take up to tens of milliseconds. How these heterogeneous transmission delays affect communication between neuronal populations is not well known. To address this question, we have studied the dynamics of two bidirectionally delayed-coupled neuronal populations using conductance-based spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, and how this behavior is related to the phase coherence between the two populations at different frequencies. We have used spectral analysis and information theory to quantify the information exchanged between the two networks. For different transmission delays between the two coupled populations, we analyze how the local field potential and multi-unit activity calculated from one population convey information in response to a set of external inputs applied to the other population. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication provided the coupling delay, the phase lag between the populations, and the frequency of the oscillations are properly matched.     

Neuronal coherence during selective attentional processing and sensory-motor integration.

Groups of neurons synchronize their activities during a variety of conditions, but whether this synchronization is functionally relevant has remained a matter of debate. Here, we survey recent findings showing that synchronization is dynamically modulated during cognitive processes. Based on this evidence, synchronization appears to reflect a general mechanism that renders interactions among selective subsets of neurons effective. We show that neuronal synchronization predicts which sensory input is processed and how efficient it is transmitted to postsynaptic target neurons during sensory-motor integration. Four lines of evidence are presented supporting the hypothesis that rhythmic neuronal synchronization, also called neuronal coherence, underlies effective and selective neuronal communication. (1) Findings from intracellular recordings strongly suggest that postsynaptic neurons are particularly sensitive to synaptic input that is synchronized in the gamma-frequency (30-90 Hz) range. (2) Neurophysiological studies in awake animals revealed enhanced rhythmic synchronization among neurons encoding task-relevant information. (3) The trial-by-trial variation in the precision of neuronal synchronization predicts part of the trial-by-trial variation in the speed of visuo-motor integration. (4) The planning and selection of specific movements can be predicted by the strength of coherent oscillations among local neuronal groups in frontal and parietal cortex. Thus, neuronal coherence appears as a neuronal substrate of an effective neuronal communication structure that dynamically links neurons into functional groups processing task-relevant information and selecting appropriate actions during attention and effective sensory-motor integration.     

Synchronous and asynchronous bursting states: role of intrinsic neural dynamics

Brain signals such as local field potentials often display gamma-band oscillations (30-70 Hz) in a variety of cognitive tasks. These oscillatory activities possibly reflect synchronization of cell assemblies that are engaged in a cognitive function. A type of pyramidal neurons, i.e., chattering neurons, show fast rhythmic bursting (FRB) in the gamma frequency range, and may play an active role in generating the gamma-band oscillations in the cerebral cortex. Our previous phase response analyses have revealed that the synchronization between the coupled bursting neurons significantly depends on the bursting mode that is defined as the number of spikes in each burst. Namely, a network of neurons bursting through a Ca(2+)-dependent mechanism exhibited sharp transitions between synchronous and asynchronous firing states when the neurons exchanged the bursting mode between singlet, doublet and so on. However, whether a broad class of bursting neuron models commonly show such a network behavior remains unclear. Here, we analyze the mechanism underlying this network behavior using a mathematically tractable neuron model. Then we extend our results to a multi-compartment version of the NaP current-based neuron model and prove a similar tight relationship between the bursting mode changes and the network state changes in this model. Thus, the synchronization behavior couples tightly to the bursting mode in a wide class of networks of bursting neurons.     

Theta band zero-lag long-range cortical synchronization via hippocampal dynamical relaying

Growing evidence suggests that synchronization among distributed neuronal networks underlie functional integration in the brain. Neural synchronization is typically revealed by a consistent phase delay between neural responses generated in two separated sources. But the influence of a third neuronal assembly in that synchrony pattern remains largely unexplored. We investigate here the potential role of the hippocampus in determining cortico-cortical theta synchronization in different behavioral states during motor quiescent and while animals actively explore the environment. To achieve this goal, the two states were modeled with a recurrent network involving the hippocampus, as a relay element, and two distant neocortical sites. We found that cortico-cortical neural coupling accompanied higher hippocampal theta oscillations in both behavioral states, although the highest level of synchronization between cortical regions emerged during motor exploration. Local field potentials recorded from the same brain regions qualitatively confirm these findings in the two behavioral states. These results suggest that zero-lag long-range cortico-cortical synchronization is likely mediated by hippocampal theta oscillations in lower mammals as a function of cognitive demands and motor acts.     

Oscillatory synchronization in large-scale cortical networks predicts perception

Normal brain function requires the dynamic interaction of functionally specialized but widely distributed cortical regions. Long-range synchronization of oscillatory signals has been suggested to mediate these interactions within large-scale cortical networks, but direct evidence is sparse. Here we show that oscillatory synchronization is organized in such large-scale networks. We implemented an analysis approach that allows for imaging synchronized cortical networks and applied this technique to EEG recordings in humans. We identified two networks: beta-band synchronization (~20 Hz) in a fronto-parieto-occipital network and gamma-band synchronization (~80 Hz) in a centro-temporal network. Strong perceptual correlates support their functional relevance: the strength of synchronization within these networks predicted the subjects' perception of an ambiguous audiovisual stimulus as well as the integration of auditory and visual information. Our results provide evidence that oscillatory neuronal synchronization mediates neuronal communication within frequency-specific, large-scale cortical networks.     

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.     

Occipital Alpha Activity during Stimulus Processing Gates the Information Flow to Object-Selective Cortex

Given the limited processing capabilities of the sensory system, it is essential that attended information is gated to downstream areas, whereas unattended information is blocked. While it has been proposed that alpha band (8–13 Hz) activity serves to route information to downstream regions by inhibiting neuronal processing in task-irrelevant regions, this hypothesis remains untested. Here we investigate how neuronal oscillations detected by electroencephalography in visual areas during working memory encoding serve to gate information reflected in the simultaneously recorded blood-oxygenation-level-dependent (BOLD) signals recorded by functional magnetic resonance imaging in downstream ventral regions. We used a paradigm in which 16 participants were presented with faces and landscapes in the right and left hemifields; one hemifield was attended and the other unattended. We observed that decreased alpha power contralateral to the attended object predicted the BOLD signal representing the attended object in ventral object-selective regions. Furthermore, increased alpha power ipsilateral to the attended object predicted a decrease in the BOLD signal representing the unattended object. We also found that the BOLD signal in the dorsal attention network inversely correlated with visual alpha power. This is the first demonstration, to our knowledge, that oscillations in the alpha band are implicated in the gating of information from the visual cortex to the ventral stream, as reflected in the representationally specific BOLD signal. This link of sensory alpha to downstream activity provides a neurophysiological substrate for the mechanism of selective attention during stimulus processing, which not only boosts the attended information but also suppresses distraction. Although previous studies have shown a relation between the BOLD signal from the dorsal attention network and the alpha band at rest, we demonstrate such a relation during a visuospatial task, indicating that the dorsal attention network exercises top-down control of visual alpha activity.     

The influence of the astrocyte field on neuronal dynamics and synchronization

Astrocytes can sense local synaptic release of glutamate by metabotropic glutamate receptors. Receptor activation in turn can mediate transient increases of astrocytic intracellular calcium concentration through inositol 1,4,5-trisphosphate production. Notably, the perturbation of calcium concentration can propagate to other adjacent astrocytes. Astrocytic calcium signaling can therefore be linked to synaptic information transfer between neurons. On the other hand, astrocytes can also modulate neuronal activity by feeding back onto synaptic terminals in a fashion that depends on their intracellular calcium concentration. Thus, astrocytes can also be active partners in neuronal network activity. The aim of our study is to provide a computationally simple network model of mutual neuron–astrocyte interactions, in order to investigate the possible roles of astrocytes in neuronal network dynamics. In particular, we focus on the information entropy of neuronal firing of the whole network, considering how it could be affected by neuron–glial interactions.     

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation

 Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train. Received: 30 March 1993/Accepted in revised form: 16 April 1994     

Learning-Induced Synchronization and Plasticity of a Developing Neural Network

Learning-induced synchronization of a neural network at various developing stages is studied by computer simulations using a pulse-coupled neural network model in which the neuronal activity is simulated by a one-dimensional map. Two types of Hebbian plasticity rules are investigated and their differences are compared. For both models, our simulations show a logarithmic increase in the synchronous firing frequency of the network with the culturing time of the neural network. This result is consistent with recent experimental observations. To investigate how to control the synchronization behavior of a neural network after learning, we compare the occurrence of synchronization for four networks with different designed patterns under the influence of an external signal. The effect of such a signal on the network activity highly depends on the number of connections between neurons. We discuss the synaptic plasticity and enhancement effects for a random network after learning at various developing stages.     

Dynamic effective connectivity of inter-areal brain circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities.     

Cellularly-driven differences in network synchronization propensity are differentially modulated by firing frequency

Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.     

Firing synchronization and temporal order in noisy neuronal networks

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.     

Selective Modulation of Interhemispheric Functional Connectivity by HD-tACS Shapes Perception

Oscillatory neuronal synchronization between cortical areas has been suggested to constitute a flexible mechanism to coordinate information flow in the human cerebral cortex. However, it remains unclear whether synchronized neuronal activity merely represents an epiphenomenon or whether it is causally involved in the selective gating of information. Here, we combined bilateral high-density transcranial alternating current stimulation (HD-tACS) at 40 Hz with simultaneous electroencephalographic (EEG) recordings to study immediate electrophysiological effects during the selective entrainment of oscillatory gamma-band signatures. We found that interhemispheric functional connectivity was modulated in a predictable, phase-specific way: In-phase stimulation enhanced synchronization, anti-phase stimulation impaired functional coupling. Perceptual correlates of these connectivity changes were found in an ambiguous motion task, which strongly support the functional relevance of long-range neuronal coupling. Additionally, our results revealed a decrease in oscillatory alpha power in response to the entrainment of gamma band signatures. This finding provides causal evidence for the antagonistic role of alpha and gamma oscillations in the parieto-occipital cortex and confirms that the observed gamma band modulations were physiological in nature. Our results demonstrate that synchronized cortical network activity across several spatiotemporal scales is essential for conscious perception and cognition.     

Rotifer Population Dynamics in Two Coupled Habitats: Invasion of Chaos

We study the role of interactions between habitats in rotifer dynamics. We use a simple discrete-time model to simulate the interactions between neighboring habitats with different intrinsic dynamics. Being uncoupled, one habitat shows periodical oscillations of the rotifer biomass while the other one demonstrates chaotic oscillations. As a result of the exchange of rotifer biomass, chaos replaces regular oscillations. As a result, the rotifer dynamics becomes chaotic in both habitats. We show that the invasion of chaos is followed by the synchronization of the chaotic regimes of both habitats, and this synchronization increases as coupling between the habitats is increased. We also demonstrate that the biological invasion of the rotifer species, which show chaotic dynamics, to a neighboring habitat with intrinsically regular plankton dynamics leads to the invasion of chaos and the synchronization of chaotic oscillations of the plankton biomass in both the habitats.     

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks.     

Stimulating at the right time to recover network states in a model of the cortico-basal ganglia-thalamic circuit

Synchronization of neural oscillations is thought to facilitate communication in the brain. Neurodegenerative pathologies such as Parkinson’s disease (PD) can result in synaptic reorganization of the motor circuit, leading to altered neuronal dynamics and impaired neural communication. Treatments for PD aim to restore network function via pharmacological means such as dopamine replacement, or by suppressing pathological oscillations with deep brain stimulation. We tested the hypothesis that brain stimulation can operate beyond a simple “reversible lesion” effect to augment network communication. Specifically, we examined the modulation of beta band (14–30 Hz) activity, a known biomarker of motor deficits and potential control signal for stimulation in Parkinson’s. To do this we setup a neural mass model of population activity within the cortico-basal ganglia-thalamic (CBGT) circuit with parameters that were constrained to yield spectral features comparable to those in experimental Parkinsonism. We modulated the connectivity of two major pathways known to be disrupted in PD and constructed statistical summaries of the spectra and functional connectivity of the resulting spontaneous activity. These were then used to assess the network-wide outcomes of closed-loop stimulation delivered to motor cortex and phase locked to subthalamic beta activity. Our results demonstrate that the spatial pattern of beta synchrony is dependent upon the strength of inputs to the STN. Precisely timed stimulation has the capacity to recover network states, with stimulation phase inducing activity with distinct spectral and spatial properties. These results provide a theoretical basis for the design of the next-generation brain stimulators that aim to restore neural communication in disease.     

Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.     

Surprising Effects of Synaptic Excitation

Typically, excitatory synaptic coupling is thought of as an influence that accelerates and propagates firing in neuronal networks. This paper reviews recent results explaining how, contrary to these expectations, the presence of excitatory synaptic coupling can drastically slow oscillations in a network and how localized, sustained activity can arise in a network with purely excitatory coupling, without sustained inputs. These two effects stem from interactions of excitatory coupling with two different forms of intrinsic neuronal dynamics, and both serve to highlight the fact that the influence of synaptic coupling in a network depends strongly on the intrinsic properties of cells in the network.This work was partially supported by the National Science Foundation, under award DMS-0414023     

Specific Entrainment of Mitral Cells during Gamma Oscillation in the Rat Olfactory Bulb

Local field potential (LFP) oscillations are often accompanied by synchronization of activity within a widespread cerebral area. Thus, the LFP and neuronal coherence appear to be the result of a common mechanism that underlies neuronal assembly formation. We used the olfactory bulb as a model to investigate: (1) the extent to which unitary dynamics and LFP oscillations can be correlated and (2) the precision with which a model of the hypothesized underlying mechanisms can accurately explain the experimental data. For this purpose, we analyzed simultaneous recordings of mitral cell (MC) activity and LFPs in anesthetized and freely breathing rats in response to odorant stimulation. Spike trains were found to be phase-locked to the gamma oscillation at specific firing rates and to form odor-specific temporal patterns. The use of a conductance-based MC model driven by an approximately balanced excitatory-inhibitory input conductance and a relatively small inhibitory conductance that oscillated at the gamma frequency allowed us to provide one explanation of the experimental data via a mode-locking mechanism. This work sheds light on the way network and intrinsic MC properties participate in the locking of MCs to the gamma oscillation in a realistic physiological context and may result in a particular time-locked assembly. Finally, we discuss how a self-synchronization process with such entrainment properties can explain, under experimental conditions: (1) why the gamma bursts emerge transiently with a maximal amplitude position relative to the stimulus time course; (2) why the oscillations are prominent at a specific gamma frequency; and (3) why the oscillation amplitude depends on specific stimulus properties. We also discuss information processing and functional consequences derived from this mechanism.