Conduction delays can enhance formation of up and down states in spiking neuronal networks

Esir, P.M.; Gordleeva, Susanna; Simonov, Alexander; Pisarchik, Alexander N.; Kazantsev, Victor B.

doi:10.1103/physreve.98.052401

Cited by 30 publications

(15 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Neural network consists of 100 excitatory synaptically coupled Hodgkin-Huxley neurons (Hodgkin and Huxley, 1952; Esir et al, 2018). We use random coupling topology with connection probability for each pair of neurons equal to 20% (Braitenberg and Schüz, 1998).…”

Section: Methodsmentioning

confidence: 99%

Astrocyte as Spatiotemporal Integrating Detector of Neuronal Activity

et al. 2019

Self Cite

View full text Add to dashboard Cite

The functional role of astrocyte calcium signaling in brain information processing was intensely debated in recent decades. This interest was motivated by high resolution imaging techniques showing highly developed structure of distal astrocyte processes. Another point was the evidence of bi-directional astrocytic regulation of neuronal activity. To analyze the effects of interplay of calcium signals in processes and in soma mediating correlations between local signals and the cell-level response of the astrocyte we proposed spatially extended model of the astrocyte calcium dynamics. Specifically, we investigated how spatiotemporal properties of Ca 2+ dynamics in spatially extended astrocyte model can coordinate (e.g., synchronize) networks of neurons and synapses.

show abstract

Section: Methodsmentioning

confidence: 99%

Astrocyte as Spatiotemporal Integrating Detector of Neuronal Activity

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…The model provides a basis for possible modifications in order to apply integrated information concepts to systems exhibiting similar, but more complicated behavior (in particular, to neuronal [ 26 , 27 , 28 , 29 ] and neuron–astrocyte [ 24 , 30 ] networks). Such modifications might incorporate non-trivial spatial patterns in bursting, and causal interactions within and between the spiking and bursting subsystems.…”

Section: Resultsmentioning

confidence: 99%

“…In this way, the inequality (33) together with the asymptotic estimate (38) supplemented by its applicability range (36) specifies the region in the parameter space of the system, where the "whole minus sum" II is positive regardless of the internal system structure (sufficient condition). The internal structure (though still without spike correlations across the system) is taken into account by the necessary and sufficient condition (27) for positive II.…”

Section: Discussionmentioning

confidence: 99%

“…Expanding the set of s in (27) to the whole definition domain of f (s) (26) leads to a sufficient (generally, stronger) condition for positive II…”

Section: Determining the Sign Of The "Whole Minus Sum" Informationmentioning

confidence: 99%

“…Note that by construction, the function g(s 1 ) defined in (30b) expresses effective information Φ eff from (3) for the hypothetic bipartition characterized by s A = s B = √ s 1 , which may or may not exist in the actual particular system. If such "symmetric" bipartition exists, then the value s A = √ s 1 belongs to the set {s A } in (27), which implies that (29) (same as (30)) is equivalent not only to (28), but also to the necessary and sufficient condition (27). Otherwise, (28) (equivalently, (29) or (30)), formally being only sufficient, still may produce a good estimate of the necessary and sufficient condition in cases when {s A } contains values which are close to √ s 1 (corresponding to nearly symmetric partitions, if such exist).…”

Section: Determining the Sign Of The "Whole Minus Sum" Informationmentioning

confidence: 99%

See 2 more Smart Citations

Integrated Information in the Spiking–Bursting Stochastic Model

Kanakov

Gordleeva

Zaikin

2020

Entropy

View full text Add to dashboard Cite

Integrated information has been recently suggested as a possible measure to identify a necessary condition for a system to display conscious features. Recently, we have shown that astrocytes contribute to the generation of integrated information through the complex behavior of neuron–astrocyte networks. Still, it remained unclear which underlying mechanisms governing the complex behavior of a neuron–astrocyte network are essential to generating positive integrated information. This study presents an analytic consideration of this question based on exact and asymptotic expressions for integrated information in terms of exactly known probability distributions for a reduced mathematical model (discrete-time, discrete-state stochastic model) reflecting the main features of the “spiking–bursting” dynamics of a neuron–astrocyte network. The analysis was performed in terms of the empirical “whole minus sum” version of integrated information in comparison to the “decoder based” version. The “whole minus sum” information may change sign, and an interpretation of this transition in terms of “net synergy” is available in the literature. This motivated our particular interest in the sign of the “whole minus sum” information in our analytical considerations. The behaviors of the “whole minus sum” and “decoder based” information measures are found to bear a lot of similarity—they have mutual asymptotic convergence as time-uncorrelated activity increases, and the sign transition of the “whole minus sum” information is associated with a rapid growth in the “decoder based” information. The study aims at creating a theoretical framework for using the spiking–bursting model as an analytically tractable reference point for applying integrated information concepts to systems exhibiting similar bursting behavior. The model can also be of interest as a new discrete-state test bench for different formulations of integrated information.

show abstract