A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

Gast, Richard; Schmidt, Helmut; Knösche, Thomas R.

doi:10.1101/806273

Cited by 3 publications

(6 citation statements)

References 32 publications

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“…We have constructed a model that maps the activity of an infinite number of coupled neurons, each described by a simple phase-oscillator equation, into the mean field firing rate and membrane potential variables. Future applications allow the possibility of including synaptic dynamics [41,42], adaptation [43], excitatory versus inhibitory populations [31,44,45], among others.…”

Section: Discussionmentioning

confidence: 99%

Neuronal cascades shape whole-brain functional dynamics at rest

Rabuffo

Fousek

Bernard

et al. 2020

Preprint

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At rest, mammalian brains display a rich complex spatiotemporal behavior, which is reminiscent of healthy brain function and has provided nuanced understandings of several major neurological conditions. Despite the increasingly detailed phenomenological documentation of the brain’s resting state, its principle underlying causes remain unknown. To establish causality, we link structurally defined features of a brain network model to neural activation patterns and their variability. For the mouse, we use a detailed connectome-based model and simulate the resting state dynamics for neural sources and whole brain imaging signals (Blood-Oxygen-Level-Dependent (BOLD), Electroencephalography (EEG)). Under conditions of near-criticality, characteristic neuronal cascades form spontaneously and propagate through the network. The largest neuronal cascades produce short-lived but robust co-fluctuations at pairs of regions across the brain. During these co-activation episodes, long-lasting functional networks emerge giving rise to epochs of stable resting state networks correlated in time. Sets of neural cascades are typical for a resting state network, but different across. We experimentally confirm the existence and stability of functional connectivity epochs comprising BOLD co-activation bursts in mice (N=19). We further demonstrate the leading role of the neuronal cascades in a simultaneous EEG/fMRI data set in humans (N=15), explaining a large part of the variability of functional connectivity dynamics. We conclude that short-lived neuronal cascades are a major robust dynamic component contributing to the organization of the slowly evolving spontaneous fluctuations in brain dynamics at rest.

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Section: Discussionmentioning

confidence: 99%

Neuronal cascades shape whole-brain functional dynamics at rest

Rabuffo

Fousek

Bernard

et al. 2020

Preprint

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“…However, to achieve a general description of this characteristic, an analytical approach is needed. Although an analytical approach to a multibody system with nonlinear dynamics is difficult, the recent progress reported in the studies of the Fokker-Planck equations in spiking neural networks [90], [91] might provide an effective solution for this purpose. In addition, the neural activity in this study was induced by random input spikes from the Poisson process.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution

Nobukawa

Nishimura

Wagatsuma

et al. 2021

IEEE Trans. Neural Netw. Learning Syst.

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Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( 1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.

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“…Thus, our model lends itself to multi-scale approaches. It can easily be extended by additional biological details, such as plasticity mechanisms (Gast et al, 2020) or gap junctions (Pietras et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

“…We are aware that the all-to-all coupling and infinite population sizes are in contrast to the actual GPe structure (Wilson, 2013;Hegeman et al, 2016). However, it has been recently shown that the mean-field model predictions can generalize to a fairly wide range of network sizes and coupling probabilities (Gast et al, 2020). Even for QIF networks with recurrent coupling probabilities of 1%, the authors found that population sizes of N = 8000 neurons were sufficient to accurately reproduce the macroscopic dynamics predicted by the mean-field model.…”

Section: Model Definition Mathematical Formulation Of Population Dynamentioning

confidence: 99%

“…In Parkinson's disease (PD), synchronized oscillations have been reported throughout all major BG nuclei (Wichmann, 2019) including the GPe (Wichmann and Soares, 2006;Mallet et al, 2008). These oscillations are characterized by transient power increases in the beta frequency band (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and an increased phase-amplitude coupling between the phase of a beta signal and the amplitude of a high-frequency gamma signal (50-250 Hz) (Jenkinson et al, 2013;Lofredi et al, 2019;Gong et al, 2020). Computational models of BG phase transitions in PD suggest that the GPe is involved in the oscillation generation, either via its recurrent coupling with the subthalamic nucleus (STN) or via its processing of inputs from striatum (STR) (Pavlides et al, 2015;Schroll and Hamker, 2016;Rubin, 2017).…”

Section: Introductionmentioning

confidence: 99%

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On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

Gast

Gong

Schmidt

et al. 2021

Preprint

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The external pallidum (GPe) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input.We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of the intra-pallidal connectivity on the GPe dynamics. We find that under healthy conditions, the inhibitory coupling determines whether the GPe is close to either a bi-stable or an oscillatory regime. Furthermore, we show that oscillatory input to the GPe, arriving from subthalamic nucleus or striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic gamma rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled type-I excitable GPe neurons.Significant StatementOur work provides (a) insight into the theoretical implications of a dichotomous GPe organization for its macroscopic dynamic regimes, and (b) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Due to the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.

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A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

Cited by 3 publications

References 32 publications

Neuronal cascades shape whole-brain functional dynamics at rest

Neuronal cascades shape whole-brain functional dynamics at rest

Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

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