Synchronization In Neuronal Networks Research Articles

Synchronization, Stochasticity, and Phase Waves in Neuronal Networks With Spatially-Structured Connectivity.

Oscillations in the beta/low gamma range (10–45 Hz) are recorded in diverse neural structures. They have successfully been modeled as sparsely synchronized oscillations arising from reciprocal interactions between randomly connected excitatory (E) pyramidal cells and local interneurons (I). The synchronization of spatially distant oscillatory spiking E–I modules has been well-studied in the rate model framework but less so for modules of spiking neurons. Here, we first show that previously proposed modifications of rate models provide a quantitative description of spiking E–I modules of Exponential Integrate-and-Fire (EIF) neurons. This allows us to analyze the dynamical regimes of sparsely synchronized oscillatory E–I modules connected by long-range excitatory interactions, for two modules, as well as for a chain of such modules. For modules with a large number of neurons (> 105), we obtain results similar to previously obtained ones based on the classic deterministic Wilson-Cowan rate model, with the added bonus that the results quantitatively describe simulations of spiking EIF neurons. However, for modules with a moderate (~ 104) number of neurons, stochastic variations in the spike emission of neurons are important and need to be taken into account. On the one hand, they modify the oscillations in a way that tends to promote synchronization between different modules. On the other hand, independent fluctuations on different modules tend to disrupt synchronization. The correlations between distant oscillatory modules can be described by stochastic equations for the oscillator phases that have been intensely studied in other contexts. On shorter distances, we develop a description that also takes into account amplitude modes and that quantitatively accounts for our simulation data. Stochastic dephasing of neighboring modules produces transient phase gradients and the transient appearance of phase waves. We propose that these stochastically-induced phase waves provide an explanative framework for the observations of traveling waves in the cortex during beta oscillations.

Effect of topology upon relay synchronization in triplex neuronal networks.

Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize due to signal propagation via relay layers. In this work, we investigate relay synchronization of partial synchronization patterns like chimera states in three-layer networks of interacting FitzHugh-Nagumo oscillators. We demonstrate that the phenomenon of relay synchronization is robust to topological random inhomogeneities of small-world type in the layer networks. We show that including randomness in the connectivity structure either of the remote network layers or of the relay layer increases the range of interlayer coupling strength where relay synchronization can be observed.

Constitutive deletion of astrocytic connexins aggravates kainate-induced epilepsy.

The astroglial gap junctional network formed by connexin (Cx) channels plays a central role in regulating neuronal activity and network synchronization. However, its involvement in the development and progression of epilepsy is not yet understood. Loss of interastrocytic gap junction (GJ) coupling has been observed in the sclerotic hippocampus of patients with mesial temporal lobe epilepsy (MTLE) and in mouse models of MTLE, leading to the suggestion that it plays a causative role in the pathogenesis. To further elucidate this clinically relevant question, we investigated consequences of astrocyte disconnection on the time course and severity of kainate-induced MTLE with hippocampal sclerosis (HS) by comparing mice deficient for astrocytic Cx proteins with wild-type mice (WT). Continuous telemetric EEG recordings and video monitoring performed over a period of 4 weeks after epilepsy induction revealed substantially higher seizure and interictal spike activity during the chronic phase in Cx deficient versus WT mice, while the severity of status epilepticus was not different. Immunohistochemical analysis showed that, despite the elevated chronic seizure activity, astrocyte disconnection did not aggravate the severity of HS. Indeed, the extent of CA1 pyramidal cell loss was similar between the experimental groups, while astrogliosis, granule cell dispersion, angiogenesis, and microglia activation were even reduced in Cx deficient as compared to WT mice. Interestingly, seizure-induced neurogenesis in the adult dentate gyrus was also independent of astrocytic Cxs. Together, our data indicate that constitutive loss of GJ coupling between astrocytes promotes neuronal hyperexcitability and attenuates seizure-induced histopathological outcomes.

Columnar grouping preserves synchronization in neuronal networks with distance-dependent time delays.

Neuronal connectivity at the cellular level in the cerebral cortex is far from random, with characteristics that point to a hierarchical design with intricately connected neuronal clusters. Here we investigate computationally the effects of varying neuronal cluster connectivity on network synchronization for two different spatial distributions of clusters: one where clusters are arranged in columns in a grid and the other where neurons from different clusters are spatially intermixed. We characterize each case by measuring the degree of neuronal spiking synchrony as a function of the number of connections per neuron and the degree of intercluster connectivity. We find that in both cases as the number of connections per neuron increases, there is an asynchronous to synchronous transition dependent only on intrinsic parameters of the biophysical model. We also observe in both cases that with very low intercluster connectivity clusters have independent firing dynamics yielding a low degree of synchrony. More importantly, we find that for a high number of connections per neuron but intermediate intercluster connectivity, the two spatial distributions of clusters differ in their response where the clusters in a grid have a higher degree of synchrony than the clusters that are intermixed.

Time delayed chemical synapses and synchronization in multilayer neuronal networks with ephaptic inter-layer coupling

In this paper, a three-layer neuronal network is studied to consider different complex connections between the neurons. In the nervous system, the communication between the neurons is mostly based on the electrical and chemical synapses. However, extracellular electric fields can induce a magnetic flux which can lead to indirect neural communications, by means of electromagnetic induction. This mode of coupling is called ephaptic coupling, which here is used between the layer. To describe the coupling within the layers, the electrical and chemical synapses are defined. We also take into account the partial time delays, to reflect the required time for information transmission through chemical synapses. Particularly, we consider partial and full time delays, as well as strong and weak coupling strengths. It is shown that three layers typically have opposite synchronization properties in the strong and weak coupling regimes. Specifically, when the coupling is strong, the top and bottom layers are synchronous, while the middle layer is desynchronous. But when the coupling is weak, the middle layer is synchronous, while the top and bottom layers are desynchronous. In overall, the most synchrony is obtained when the weak coupling is accompanied with partial time delays in chemical communications. Our research sheds new light on the complex interplay between the time delay, the ephaptic coupling, and the synchronization in neuronal networks.

Synchronization and Rhythm Transition in a Complex Neuronal Network

Synchronization and rhythm transition in an excitatory-inhibitory balanced cortical neuronal network are investigated in this paper. A small-world neuronal network is performed to be the cortical region of cerebral cortex, which is composed of different types of Izhikevich neurons. The combination of regular spiking (RS) cells, chattering (CH) cells, or mixed RS and CH cells are imitated as excitatory neurons, whereas fast spiking (FS) cells mimic inhibitory neurons. We mainly focus on the effect of different types of neurons on synchronization and rhythm transition of the neuronal network. The simulation results illustrate that it is easier for the neuronal network with CH excitatory neurons to achieve synchronization, and it is also more susceptible to the parameters than the network with RS neurons. Together with the weight of the synaptic connection, the structure of the small-world network is also explored to identify its influence on the synchronization and the rhythm transition. Moreover, we found that the synchronization performance could be improved by increasing the degree of influence among neurons. Importantly, the synchronization states are associated with the rhythm transitions. Especially, the consistency of synchronization of the neuronal network and y band rhythm is illustrated. In addition, our results could have an important significance on further understanding brain rhythms and synchrony in neuroscience.

Potassium channel dysfunction in human neuronal models of Angelman syndrome

Disruptions in the ubiquitin protein ligase E3A (UBE3A) gene cause Angelman syndrome (AS). Whereas AS model mice have associated synaptic dysfunction and altered plasticity with abnormal behavior, whether similar or other mechanisms contribute to network hyperactivity and epilepsy susceptibility in AS patients remains unclear. Using human neurons and brain organoids, we demonstrate that UBE3A suppresses neuronal hyperexcitability via ubiquitin-mediated degradation of calcium- and voltage-dependent big potassium (BK) channels. We provide evidence that augmented BK channel activity manifests as increased intrinsic excitability in individual neurons and subsequent network synchronization. BK antagonists normalized neuronal excitability in both human and mouse neurons and ameliorated seizure susceptibility in an AS mouse model. Our findings suggest that BK channelopathy underlies epilepsy in AS and support the use of human cells to model human developmental diseases.

Hyperexcitable neurons in brain organoids

Neurodevelopment Individuals with Angelman syndrome experience intellectual disability and seizures throughout their lives. In this condition, ubiquitin-mediated degradation of a key potassium channel is disrupted, allowing for the neuronal excitability and network synchronization that leads to seizure. Sun et al. used brain organoid technology to study what happens in human neurons with a mutation in a ubiquitin ligase that is implicated in Angelman syndrome. In these in vitro models and in a mouse model of Angelman syndrome, antagonists for the potassium channel normalized neuronal excitability. Science , this issue p. [1486][1] [1]: /lookup/doi/10.1126/science.aav5386

Synchronization and chimera states in a multilayer neuronal network with unidirectional interlayer links

The brain consists of many interconnected systems and subsystems that have unidirectional or bidirectional connectivities. In this paper, we consider a two-layer neuronal network with unidirectional interlayer connections to investigate the effects of one layer on the other one. Two one-dimensional ring networks with non-local couplings construct the two-layer network. The couplings are considered to be linear to describe the electrical synapses. At first, the independent layer, which is not affected by the other layer, is analysed. Different patterns such as synchronizations, non-stationary chimera state and imperfect synchronization are observed in such solo network. Then the two-layer network is investigated by varying three coupling strengths of intra-layer and inter-layer links. The results show that the first layer can change the behaviour of neurons in the second layer according to the values of coupling strengths. The interaction of the interlayer and intralayer couplings can also induce the emergence of imperfect chimera state, which was not observed in the monolayer network. These self-organized phenomena can have strong relations with brain functions and malfunctions.

Geometric analysis of synchronization in neuronal networks with global inhibition and coupling delays.

We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behaviour. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled with time-delayed synapses. The excitatory population is uncoupled, while the inhibitory population is tightly coupled without time delay. A geometric singular perturbation analysis yields existence and stability conditions for periodic solutions where the excitatory cells are synchronized and different phase relationships between the excitatory and inhibitory populations can occur, along with formulae for the periods of such solutions. In particular, we show that if there are no delays in the coupling, oscillations where the excitatory population is synchronized cannot occur. Numerical simulations are conducted to supplement and validate the analytical results. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Necessary Conditions for Complete Synchronization of a Coupled Chaotic Aihara Neuron Network with Electrical Synapses

In this paper, the synchronization problem of a chaotic Aihara neuron network is considered. Based on the master stability function (MSF) analysis, some necessary conditions are proposed to investigate the complete synchronization of the electrical coupled chaotic Aihara neuron networks. Especially, the two-dimensional parameter-space plots are obtained numerically to visualize the possible synchronized region. For the chaotic Rulkov neuron network, the numerical simulations of the MSF show that complete synchronization of the electrical coupled Aihara neuron network can be achieved when the coupling strength lies in a suitable interval, while it is highly improbable to attain complete synchronization when all neurons are in the chaotic bursting. Moreover, the complete synchronization cannot be reached with further increase or decrease of coupling strength. These results are probably common features as far as discrete-time neuron networks are concerned. Finally, based on the drive-response active control method, an LMI-based criterion is obtained to ensure complete synchronization of the available chaotic Aihara neuron network. The spatiotemporal patterns measured by the state distribution of neurons are employed to validate the effectiveness of our control scheme.

Two-fold effects of inhibitory neurons on the onset of synchronization in Izhikevich neuronal networks

Synchronization is a widely studied phenomenon in neuroscience. The ever-increasing morbidity of brain diseases makes the investigation on this topic significant in both psychology and medicine. In this paper, we consider an Izhikevich neuronal network composed of both excitatory and inhibitory neurons, and introduce the Tsodyks-Uziel-Markram (TUM) model of neuronal transmission. To study the impact of inhibitory neurons in the synchronization, we make comparative studies by considering the inhibitory neurons could fire either spontaneously or not in the network. Simulation results exemplify that the synchronized system shows different periodic-like oscillatory patterns of multi-stripes. We find that the inhibitory neurons have two-fold impacts on the oscillatory patterns. On the one hand, they can delay the firing of the neurons, deleterious for synchronization. On the other hand, they are able to facilitate the transition of the oscillatory patterns, beneficial for synchronization.

Delay-induced synchronization transition in a small-world neuronal network of FitzHugh–Nagumo neurons subjected to sine-Wiener bounded noise

Noise and delay are ubiquitous in brain and they have significant effects on neuronal network synchronization and even brain functions. Based on a small-world neuronal network of delayed FitzHugh–Nagumo (FHN) neurons subjected to sine-Wiener (SW) bounded noise, the effects of delay and SW noise on synchronization and synchronization transition are numerically investigated by calculating a synchronization measure R and plotting spatiotemporal patterns. The phenomenon of delay-induced synchronization transition is observed as delay [Formula: see text] is increased. And large self-correlation time and strength of SW noise can increase the number of delay-induced synchronization transition. In addition, delay-induced synchronization transition is robust against the change of topology structure of neuronal network and this phenomenon becomes much easier to see for small nearest neighbors k in the small-world network. Since synchronization transition may imply functional switch, our results may have important implications, and inspire future studies.

Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks

Most previous studies assumed noise to be unbounded Gaussian. Here the effects of non-Gaussian cross-correlated sine-Wiener (CCSW) bounded noises on temporal regularity and spatial synchronization of coupled neurons are investigated in regular and small-world networks of the FitzHugh–Nagumo (FHN) neurons. For regular neuronal networks, as cross-correlation time of CCSW noises is increased, CCSW noises-induced temporal coherent resonance occurs at appropriately cross-correlation time of CCSW noises, and spatial synchronization in neuronal network is always impaired. In addition, the increasing degree of correlation of CCSW noises may enhance or impair temporal regularity, which is dependent on cross-correlation time. On the other hand, the increasing degree of correlation of CCSW noises destroys spatial synchronization or has no effect on spatial synchronization. For small world neuronal network, CCSW noises-induced enhancement of temporal regularity and degradation of spatial synchronization are still observed. Furthermore, the increasing rewiring probability make spatiotemporal pattern more order in time and in space. If delay is introduced into small world network, the aforementioned CCSW noises-induced phenomena still exist. Meanwhile, delay let spatiotemporal pattern more disorder.

Synchronization in a temporal multiplex neuronal hypernetwork

Synchronization in time-varying complex dynamical systems has been explored in a variety of different coupling topologies during the last two decades. In most of the previous cases, the basic time-varying coupling topologies were considered to be a single interaction between the nodes or in a monolayer configuration, although in many real situations the types of interactions are more than one or in the form of multilayer. In this work, we study the synchronization in multiplex neuronal network, which evolves with time, and each layer consists of more than one interaction function. Specifically, we consider a neuronal hypernetwork at each layer in which neurons are communicated with each other via electrical and chemical synapses simultaneously and independently. The network corresponding to the electrical gap junctional coupling form a small-world network while the connection associated with the chemical synaptic interaction forms a unidirectional random network. Then intralayer connections are allowed to switch stochastically over time with a characteristic rewiring frequency, whereas interlayer connections via electrical synapses are time invariant. We explore the intralayer and interlayer neuronal synchrony in such network and analytically derive the necessary stability conditions for synchrony using master stability function approach, and excellently match with our numerical findings. Interestingly, we find that the higher frequency of switching links in the intralayer enhances both intralayer and interlayer synchrony and conferring larger windows of synchrony. We also analyze the robustness of these synchronization states with respect to initial conditions using the basin stability framework. Furthermore we find that rapidly changing networks take much less time to reach synchronization state. Lastly, we inspect the dynamical robustness of interlayer synchronization against stochastic demultiplexing of each replica, with analytical justification.

Beta-Rhythm Oscillations and Synchronization Transition in Network Models of Izhikevich Neurons: Effect of Topology and Synaptic Type

Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike regularly with beta rhythms. We find a wide range of behavior including continuous transition, explosive transition, as well as lack of global order. The stronger electrical synapses are more conducive to synchronization and can even lead to explosive synchronization. The key network element which determines the order of transition is found to be the clustering coefficient and not the small world effect, or the existence of hubs in a network. These results are in contrast to previous results which use phase oscillator models such as the Kuramoto model. Furthermore, we show that the patterns of synchronization changes when one goes to the gamma band. We attribute such a change to the change in the refractory period of Izhikevich neurons which changes significantly with frequency.

A Novel Microbiosensor Microarray for Continuous ex Vivo Monitoring of Gamma-Aminobutyric Acid in Real-Time.

Gamma-aminobutyric acid (GABA) is a major inhibitory neurotransmitter that is essential for normal brain function. It is involved in multiple neuronal activities, including plasticity, information processing, and network synchronization. Abnormal GABA levels result in severe brain disorders and therefore GABA has been the target of a wide range of drug therapeutics. GABA being non-electroactive is challenging to detect in real-time. To date, GABA is detected mainly via microdialysis with a high-performance liquid chromatography (HPLC) system that employs electrochemical (EC) and spectroscopic methodology. However, these systems are bulky and unsuitable for real-time continuous monitoring. As opposed to microdialysis, biosensors are easy to miniaturize and are highly suitable for in vivo studies; they selectively oxidize GABA into a secondary electroactive product (usually hydrogen peroxide, H2O2) in the presence of enzymes, which is then detected by amperometry. Unfortunately, this method requires a rather cumbersome process with prereactors and relies on externally applied reagents. Here, we report the design and implementation of a GABA microarray probe that operates on a newly conceived principle. It consists of two microbiosensors, one for glutamate (Glu) and one for GABA detection, modified with glutamate oxidase and GABASE enzymes, respectively. By simultaneously measuring and subtracting the H2O2 oxidation currents generated from these microbiosensors, GABA and Glu can be detected continuously in real-time in vitro and ex vivo and without the addition of any externally applied reagents. The detection of GABA by this probe is based upon the in-situ generation of α-ketoglutarate from the Glu oxidation that takes place at the Glu microbiosensor. A GABA sensitivity of 36 ± 2.5 pA μM-1cm-2, which is 26-fold higher than reported in the literature, and a limit of detection of 2 ± 0.12 μM were achieved in an in vitro setting. The GABA probe was successfully tested in an adult rat brain slice preparation. These results demonstrate that the developed GABA probe constitutes a novel and powerful neuroscientific tool that could be employed in the future for in vivo longitudinal studies of the combined role of GABA and Glu (a major excitatory neurotransmitter) signaling in brain disorders, such as epilepsy and traumatic brain injury, as well as in preclinical trials of potential therapeutic agents for the treatment of these disorders.

Synchronization and wave propagation in neuronal network under field coupling

Electric and chemical synapse play important role in connecting neurons and thus signal propagation can be realized between neurons. External electric stimulus can change the excitability of neuron and then the electrical activities can be modulated completely. Continuous fluctuation of ion concentration in cell can induce complex time-varying electromagnetic field during the exchange of charged ions across the membrane of neuron. Polarization and magnetization in the media (and neuron), which exposed to electromagnetic radiation, can modulate the dynamical response and mode transition in electrical activities of neurons. In this paper, magnetic flux is used to describe the effect of electromagnetic field, and the three-variable Hindmarsh-Rose neuron model is updated to propose a four-variable neuron model that the effect of electromagnetic induction and radiation can be explained. Based on the physical law of electromagnetic induction, exchange of charged ions and flow of ion currents will change the distribution of electromagnetic filed in cell, and each neuron will be exposed to the superimposed field triggered by other neurons. Therefore, signal exchange could occur even synapse coupling between neurons is removed in the case of field coupling. A chain network is proposed to investigate the signal exchange between neurons under field coupling when synapse coupling is not available. It is found that field coupling between neurons can change the collective behaviors in electrical activities. A statistical factor of synchronization and spatial patterns are calculated, these results confirmed that field coupling is effective for signal communication between neurons. In the end, open problems are suggested for readers’ extensive guidance in this field.

Neuropeptide Y affects thalamic reticular nucleus neuronal firing and network synchronization associated with suppression of spike-wave discharges.

Neuropeptide Y (NPY) potently suppresses spike-wave discharges (SWDs) in a genetic rat model of absence epilepsy (GAERS), but the underlying neurophysiologic mechanisms are not clear. We therefore sought to determine the in vivo effects of NPY on neuronal firing in the cortico-thalamo-cortical network activity, known to play a critical role in the generation of SWDs in these rats. NPY was administered intracerebroventricularly (ICV) or in separate experiments locally on the neurons of caudal thalamic reticular nucleus (NRT) by use of juxtacellular iontophoresis in triple-barrel electrodes in male GAERS aged 12-15 weeks, in vivo under neuroleptic anesthesia. Drug infusions and electroencephalography (EEG) monitoring were performed simultaneously with juxtacellular single neuronal recordings. Effect of NPY on electrically induced SWD induction threshold were also measured. NPY administration ICV led to a decrease in the total length of SWDs in EEG recordings. Both ICV administration and iontophoresis of NPY on NRT neurons led to an increase in interictal neuronal firing of NRT neurons. During ictal periods, ICV NPY administration reduced the number of thalamic action potentials per SWDs, as well as reduced waveform correlations between field potentials within the NRT and the cortical EEG. NPY administration ICV did not significantly alter the firing patterns of relay thalamic neurons interictally and cortical neurons during ictal and interictal periods. In addition, SWD induction threshold in the S2 region of the cortex was significantly increased after NPY administration. Our results show alterations in cortico-thalamo-cortical local and network properties following ICV administration of NPY, suggesting mechanisms of SWD suppression in GAERS. Cellular and network alteration of NRT activity, resulting from a direct action of NPY, may be a contributor to this effect.

Bifurcations and Synchronization of Delay-Coupled Neuronal Networks with Autaptic Connections

This paper focuses on the dynamic behaviors of delay-coupled networks consisting of an arbitrary number of nonidentical neurons with unidirectional connections and an electrical synapse from one neuron onto itself. The stability criteria and different types of bifurcations are discussed by decomposing and analyzing the associated characteristic equation. Then, the study turns to the validation of theoretical results through numerical simulations and various interesting neural activities are observed, such as nontrivial equilibria, different patterns of oscillations, multistability coexistence, multiple switches between the quiescent and different periodic states, and transitions between the coexisting equilibria and the coexistence of equilibria and periodic oscillations. It is shown that time delays play important roles in the system performance and can be used to control neural activities.