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

Hasegawa, Hideo

doi:10.1103/physreve.70.021912

Cited by 24 publications

(7 citation statements)

References 35 publications

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“…Future models could assess cellular-scale degeneracy in neuronal models endowed with stochastic channels, especially addressing questions about the emergence of perithreshold oscillations and the role of stochastic fluctuations within such a framework of degeneracy. Specifically, whereas noise is not considered as an essential component in the emergence of the bifurcations that result in mixed-mode oscillations (Fransén et al 2004; Rotstein 2017; Rotstein et al 2006; Rotstein et al 2008), the presence of channel noise or synaptic noise could enhance the robustness of the perithreshold oscillations or make the oscillations to be noisy sinusoids (Fransén et al 2004; Rotstein et al 2006; White et al 1998), outcomes that are consistent with the stochastic bifurcation structures (Bashkirtseva and Ryashko 2011; Berglund and Landon 2012; Gong and Xu 2001; Hasegawa 2004; Kanamaru et al 2001; Kember et al 2001; Krupa and Touboul 2016; Lindner and Schimansky-Geier 1999; Scholl et al 2005; Tanabe and Pakdaman 2001; Tuckwell 2008; Tuckwell and Rodriguez 1998; Tuckwell et al 2003).…”

Section: Discussionmentioning

confidence: 97%

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Mittal

Narayanan

2018

Journal of Neurophysiology

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Biological heterogeneities are ubiquitous and play critical roles in the emergence of physiology at multiple scales. Although neurons in layer II (LII) of the medial entorhinal cortex (MEC) express heterogeneities in channel properties, the impact of such heterogeneities on the robustness of their cellular-scale physiology has not been assessed. Here, we performed a 55-parameter stochastic search spanning nine voltage- or calcium-activated channels to assess the impact of channel heterogeneities on the concomitant emergence of 10 in vitro electrophysiological characteristics of LII stellate cells (SCs). We generated 150,000 models and found a heterogeneous subpopulation of 449 valid models to robustly match all electrophysiological signatures. We employed this heterogeneous population to demonstrate the emergence of cellular-scale degeneracy in SCs, whereby disparate parametric combinations expressing weak pairwise correlations resulted in similar models. We then assessed the impact of virtually knocking out each channel from all valid models and demonstrate that the mapping between channels and measurements was many-to-many, a critical requirement for the expression of degeneracy. Finally, we quantitatively predict that the spike-triggered average of SCs should be endowed with theta-frequency spectral selectivity and coincidence detection capabilities in the fast gamma-band. We postulate this fast gamma-band coincidence detection as an instance of cellular-scale-efficient coding, whereby SC response characteristics match the dominant oscillatory signals in LII MEC. The heterogeneous population of valid SC models built here unveils the robust emergence of cellular-scale physiology despite significant channel heterogeneities, and forms an efficacious substrate for evaluating the impact of biological heterogeneities on entorhinal network function.

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Section: Discussionmentioning

confidence: 97%

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Mittal

Narayanan

2018

Journal of Neurophysiology

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“…In [162], the dynamics of FHN neuron ensembles with time-delayed couplings subject to white noise was studied by using both direct simulations and a semi-analytical augmented moment method proposed in [163]. The effects of the parameters, including the coupling strength, delay, noise intensity and ensemble size, on the emergence of the oscillation and on the synchronization in FHN neuron ensembles were studied.…”

Section: Synchronization Of Neuron Assembles Withmentioning

confidence: 99%

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Yang

et al. 2008

Acta Mech Sin

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Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one-or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities (stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.).types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.

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“…Note that some more sophisticated MF approaches [19,27] adopt the Gaussian decoupling approximation, yet do not require a QIA, as their final form accounts for spatial averages of fluctuations of both local and global variables.…”

Section: B Formulation Of Mfasmentioning

confidence: 99%

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units

et al. 2014

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We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.

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

Cited by 24 publications

References 35 publications

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units

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