Dynamics of a large system of spiking neurons with synaptic delay

Devalle, Federico; Montbrió, Ernest; Pazó, Diego

doi:10.1103/physreve.98.042214

Cited by 54 publications

(43 citation statements)

References 75 publications

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“…In this paper we considered a model including the minimal ingredients necessary to reproduce the phenomenon of coexisting γ oscillations corresponding to quite simple (namely, periodic) collective regimes. However, the introduction of synaptic delay in the model can lead to more complex coexisting states, like quasiperiodic and even chaotic solutions, as recently shown for fully coupled networks in [63,100]. The inclusion of delay in our model can enrich the dynamical scenario, maybe allowing the mimicking of further aspects of the complex patterns of activity observed in the brain, e.g., sharp-wave ripples observed in the hippocampus which are fundamental for memory consolidation [101].…”

Section: Discussionmentioning

confidence: 77%

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

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et al. 2020

Phys. Rev. Research

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Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum γ oscillations have received particular attention due to their ubiquitous nature and their correlation with higher brain functions. Recently, it has been reported that γ oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two γ rhythms correspond to different states of the network, but their origin has been not yet clarified.Here we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast γ rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast γ rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective γ oscillations from slow to fast and vice versa. Furthermore, to draw a connection with the experimental observations, we consider the modulation of the γ rhythms induced by a slower (θ) rhythm driving the network dynamics. In this context, depending on the strength of the forcing and the noise amplitude, we observe phase-amplitude and phase-phase coupling between the fast and slow γ oscillations and the θ forcing. Phase-phase coupling reveals on average different θ-phase preferences for the two coexisting γ rhythms joined to a wide cycle-to-cycle variability.

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Section: Discussionmentioning

confidence: 77%

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Segneri

Volo

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…In this paper we considered a model including the minimal ingredients necessary to reproduce the phenomenon of coexisting gamma oscillations corresponding to quite simple (namely, periodic) collective regimes. However, the introduction of synaptic delay in the model can lead to more complex coexisting states, like quasi-periodic and even chaotic solutions, as recently shown for fully coupled networks in [65,97]. The inclusion of delay in our model can enrich the dynamical scenario maybe allowing to mimic further aspects of the complex patterns of activity observed in the brain, like e.g.…”

Section: Discussionmentioning

confidence: 79%

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Segneri

Volo

et al. 2019

Preprint

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Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to their correlation with higher brain functions. Recently, it has been reported that gamma oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two gamma rhythms correspond to dfferent states of the network, but their origin has been not yet clarified. Here, we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast gamma rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast gamma rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective gamma oscillations from slow to fast and vice versa. Furthermore, to make a closer contact with the experimental observations, we consider the modulation of the gamma rhythms induced by a slower (theta) rhythm driving the network dynamics. In this context, depending on the strength of the forcing, we observe phase-amplitude and phase-phase coupling between the fast and slow gamma oscillations and the theta forcing. Phase-phase coupling reveals different theta-phases preferences for the two coexisting gamma rhythms.

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“…A number of other studies have employed mean-field reductions for populations of QIF neurons to elucidate how microscopic neural properties affect the macroscopic dynamics [228,229]. This includes insights into networks of heterogeneous QIF neurons with time delayed, all-to-all synaptic coupling [230,231], or two such networks [232]. Moreover, the mean-field reductions are also useful to analyze spatially extended networks of both Theta and QIF neurons, where localized patterns-such as bump states-can occur; cf.…”

Section: Dynamics Of Neural Circuits and Populationsmentioning

confidence: 99%

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

et al. 2020

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Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction. Understanding how network structure and interactions, as well as the microscopic properties of individual units, shape the emerging collective dynamics is critical to find factors that lead to malfunction. However, many biological systems such as the brain consist of a large number of dynamical units. Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost. Here we review recently introduced approaches, known as the Ott-Antonsen and Watanabe-Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales. Thus, reduced model equations are obtained that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. The resulting equations are next-generation models: Rather than being heuristic, they exactly link microscopic and macroscopic descriptions and therefore accurately capture microscopic properties of the underlying system. At the same time, they are sufficiently simple to analyze without great computational effort. In the last decade, these reduction methods have become instrumental in understanding how network structure and interactions shape the collective dynamics and the emergence of synchrony. We review this progress based on concrete examples and outline possible limitations. Finally, we discuss how linking the reduced models with experimental data can guide the way towards the development of new treatment approaches, for example, for neurological disease.

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Dynamics of a large system of spiking neurons with synaptic delay

Cited by 54 publications

References 75 publications

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

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