Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

Understanding the origin, nature and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in Neuroscience. Such patterns include collective oscillations, emerging out of neural synchronization, as well as highly-heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches". Much debate has been generated about the possible scale-invariance or criticality of such avalanches, and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach, following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but, crucially, including stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-states, synchronous, asynchronous, and up-state phases, and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition, as usually assumed in theoretical approaches, but to a synchronization phase transition, at which incipient oscillations and scalefree avalanches coexist. Furthermore, our model also accounts for up and down states as they occur, e.g. during deep sleep. The present approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping shed light into basic aspects of brain functioning from a very broad perspective.Cortical dynamics | Neuronal avalanches | Criticality | Synaptic plasticity T he cerebral cortex exhibits spontaneous activity even in the absence of any task or external stimuli (1-3). A salient aspect of this, so-called, resting-state dynamics, as revealed by in vivo and in vitro measurements, is that it exhibits outbursts of electrochemical activity, characterized by brief episodes of coherence -during which many neurons fire within a narrow time window-interspaced by periods of relative quiescence, giving rise to collective oscillatory rhythms (4, 5). Shedding light on the origin, nature, and functional meaning of such an intricate dynamics is a fundamental challenge in Neuroscience (6).Upon experimentally enhancing the spatio-temporal resolution of activity recordings, Beggs and Plenz made the remarkable finding that, actually, synchronized outbursts of neural activity could be decomposed into complex spatio-temporal patterns, thereon named "neuronal avalanches" (7). The sizes and durations of such avalanches were reported to be distributed as power-laws, i.e. to be organized in a scale-free way, limited only by network size (7). Furthermore, they obey finite-size scaling (8), a trademark of scale invariance...

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“…In this case, our theory constitutes a sound mesoscopic description of existing microscopic models for up-and-down transitions (29,49,63,86).…”

Section: Conclusion and Discussionmentioning

confidence: 96%

Landau–Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Santo

Villegas

Burioni

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

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185

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“…Chaotic behavior has also been observed in several neuronal structures such as cells, synapses [26, 27], and neural networks [28–32]. Chaotic dynamics has been attributed to large scale brain activities and physiological processes [33] such as information processing [34], synaptic plasticity [35], memory [36], perceptual processing and recognition of unknown odor [37] and also brain state transitions [38].…”

Section: Introductionmentioning

confidence: 99%

Introducing chaotic codes for the modulation of code modulated visual evoked potentials (c-VEP) in normal adults for visual fatigue reduction

et al. 2019

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Code modulated Visual Evoked Potentials (c-VEP) based BCI studies usually employ m-sequences as a modulating codes for their broadband spectrum and correlation property. However, subjective fatigue of the presented codes has been a problem. In this study, we introduce chaotic codes containing broadband spectrum and similar correlation property. We examined whether the introduced chaotic codes could be decoded from EEG signals and also compared the subjective fatigue level with m-sequence codes in normal subjects. We generated chaotic code from one-dimensional logistic map and used it with conventional 31-bit m-sequence code. In a c-VEP based study in normal subjects (n = 44, 21 females) we presented these codes visually and recorded EEG signals from the corresponding codes for their four lagged versions. Canonical correlation analysis (CCA) and spatiotemporal beamforming (STB) methods were used for target identification and comparison of responses. Additionally, we compared the subjective self-declared fatigue using VAS caused by presented m-sequence and chaotic codes. The introduced chaotic code was decoded from EEG responses with CCA and STB methods. The maximum total accuracy values of 93.6 ± 11.9% and 94 ± 14.4% were achieved with STB method for chaotic and m-sequence codes for all subjects respectively. The achieved accuracies in all subjects were not significantly different in m-sequence and chaotic codes. There was significant reduction in subjective fatigue caused by chaotic codes compared to the m-sequence codes. Both m-sequence and chaotic codes were similar in their accuracies as evaluated by CCA and STB methods. The chaotic codes significantly reduced subjective fatigue compared to the m-sequence codes.

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“…dynamic changes of synaptic strength on time scales of 100 ms to 1000 ms induced by presynaptic neural activity. Theoretical studies have shown that STP exerts profound effects on network activity (Levina et al 2007;Pittorino et al 2017) and information processing capabilities (Abbott et al 1997;Fortune and Rose 2001;Merkel and Lindner 2010;Rosenbaum et al 2012;Droste et al 2013). In particular, in a recent biophysically detailed microcircuit model (Markram et al 2015), STP has been a critical factor for reproducing experimentally observed activity patterns.…”

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confidence: 99%

Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

2020

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Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting shortterm plasticity (STP). Under the assumption that spike arrivals at synapses have Poisson statistics, we derive analytically stochastic mean-field dynamics for the effective synaptic coupling between finite-size populations undergoing Tsodyks-Markram STP. The novel mean-field equations account for both finite number of synapses and correlations between the neurotransmitter release probability and the fraction of available synaptic resources. Comparisons with Monte Carlo simulations of the microscopic model show that in both feedforward and recurrent networks the mesoscopic mean-field model accurately reproduces stochastic realizations of the total synaptic input into a postsynaptic neuron and accounts for stochastic switches between Up and Down states as well as for population spikes. The extended mesoscopic population theory of spiking neural networks with STP may be useful for a systematic reduction of detailed biophysical models of cortical microcircuits to efficient and mathematically tractable mean-field models.

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Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

Cited by 19 publications

References 67 publications

Landau–Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Landau–Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Introducing chaotic codes for the modulation of code modulated visual evoked potentials (c-VEP) in normal adults for visual fatigue reduction

Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

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