Noise-induced transition in excitable neuron models

Tanabe, Seiji; Pakdaman, Khashayar

doi:10.1007/s004220100256

Cited by 26 publications

(33 citation statements)

References 27 publications

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“…[47]). Similar behavior of the membrane-potential distribution has been reported in a HH neuron model [33] [28]. When adopting the Gaussian assumption, we may express the average of fluctuations in terms of the first and second moments only.…”

Section: Neuron Ensembles a Dmf Approximationsupporting

confidence: 70%

Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises

Hasegawa

2003

Phys. Rev. E

113

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Dynamics of an ensemble of N -unit FitzHugh-Nagumo (FN) neurons subject to white noises has been studied by using a semi-analytical dynamical mean-field (DMF) theory in which the original 2N -dimensional stochastic differential equations are replaced by 8-dimensional deterministic differential equations expressed in terms of moments of local and global variables. Our DMF theory, which assumes weak noises and the Gaussian distribution of state variables, goes beyond weak couplings among constituent neurons. By using the expression for the firing probability due to an applied single spike, we have discussed effects of noises, synaptic couplings and the size of the ensemble on the spike timing precision, which is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. DMF theory is extended to a large cluster which can be divided into multiple sub-clusters according to their functions. A model calculation has shown that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy sub-clusters with feed-forward couplings, as in the synfire chain. Results calculated by our DMF theory are nicely compared to those obtained by direct simulations. A comparison of DMF theory with the conventional moment method is also discussed.

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Section: Neuron Ensembles a Dmf Approximationsupporting

confidence: 70%

Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises

Hasegawa

2003

Phys. Rev. E

113

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“…Thus noise can be used to reveal dynamical regimes of a system that are available but are hidden normally. There are several theoretical studies of noise-induced transitions in biological systems, including noise-induced transitions in Hodgkin-Huxley models of excitable membranes (Horsthemke and Lefever 1981;Tanabe and Pakdaman 2001), and noise-induced bursting in models of mammalian thermoreceptors (Huber et al 2000;Longtin and Hinzer 1996).…”

Section: Introductionmentioning

confidence: 99%

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

Neiman¹,

Yakusheva²,

Russell³

2007

Journal of Neurophysiology

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Neiman AB, Yakusheva TA, Russell DF. Noise-induced transition to bursting in responses of paddlefish electroreceptor afferents. J Neurophysiol 98: [2795][2796][2797][2798][2799][2800][2801][2802][2803][2804][2805][2806] 2007. First published September 12, 2007; doi:10.1152/jn.01289.2006. The response properties of ampullary electroreceptors of paddlefish, Polyodon spathula, were studied in vivo, as single-unit afferent responses to external electrical stimulation with varied intensities of several types of noise waveforms, all Gaussian and zero-mean. They included broadband white noise, Ornstein-Uhlenbeck noise, low-or high-frequency band-limited noise, or natural noise recorded from swarms of Daphnia zooplankton prey, or from individual prey. Normally the afferents fire spontaneously in a tonic manner, which is actually quasiperiodic due to embedded oscillators. 1) Weak noise stimuli increased the variability of afferent firing, but it remained tonic. 2) In contrast, stimulation with less-weak broadband noise led to a qualitative change of the firing patterns, to parabolic bursting, even though the mean firing rate was scarcely affected.3) The transition to afferent bursting was marked by the development of two well-separated timescales: the fast frequency of spiking inside bursts at Յ250 spikes/s and the slow frequency of burst occurrences at about 9 (range 5-13) bursts/s. These two timescales were manifested as two regimes in afferent power spectra, bimodal interspike interval histograms, return maps, and autocorrelation functions of afferent spike trains. 4) The stochastic approximately 9-Hz bursts were not simply driven by similar-frequency components of noise stimuli because bursts could be dissociated from stimulus waveforms using high-pass filtered noise, or a 0.1-Hz sine-wave stimulus. 5) Arrhenius plots showed that the threshold noise intensity required to elicit bursting depended on the frequency content of a noise stimulus, being lowest, about 1.2 V/cm, for stimuli matching the 1-to 20-Hz best response band of these cathodally excited ampullary electroreceptors. This is only slightly higher than previous behavioral estimates of the electrosensory threshold as 0.5 V/cm. 6) Comparable threshold values for bursting came from an alternate analytical approach, based on correlation times of spike trains. 7) Simultaneous recordings from pairs of afferents showed that their bursting frequencies (bursts/s) always converged as the amplitude of a noise stimulus was raised. Thus the slow timescale of bursting is similar for different electroreceptors, even though their mean spiking rates can differ. In conclusion, the ampullary electroreceptors of paddlefish have two distinct modes of operation: their spontaneous tonic firing is modulated by the weakest stimuli, but they switch to bursting output for less-weak stimuli. We propose that afferent bursting may mediate close-range tracking of planktonic prey.

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“…Numerical simulations for a single FN neuron have shown that for weak noises, the distribution of x(t) of the membrane potential nearly obeys the Gaussian distribution, although for strong noises, the distribution of x(t) deviates from the Gaussian, taking a bimodal form [26] [27]. Similar behavior of the membrane-potential distribution has been reported also in the HH neuron model [28] [29]. We express Eqs.…”

Section: A Basic Formulationmentioning

confidence: 52%

Augmented moment method for stochastic ensembles with delayed couplings. II. FitzHugh-Nagumo model

Hasegawa

2004

Phys. Rev. E

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Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For N -unit FN neuron ensembles, AMM transforms original 2N -dimensional stochastic delay differential equations (SDDEs) to infinite-dimensional deterministic DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level m in the level-m AMM (AMMm), yielding 8(m + 1)-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the fluctuation-induced enhancement at the transition between nonoscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.

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Noise-induced transition in excitable neuron models

Cited by 26 publications

References 27 publications

Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises

Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises

Noise-Induced Transition to Bursting in Responses of Paddlefish Electroreceptor Afferents

Augmented moment method for stochastic ensembles with delayed couplings. II. FitzHugh-Nagumo model

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