Dynamics of subthreshold and suprathreshold resonance modulated by hyperpolarization-activated cation current in a bursting neuron

Guan, Lei; Zhao, Zhiguo

doi:10.1007/s11071-021-06230-8

Cited by 15 publications

(4 citation statements)

References 64 publications

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“…Therefore, a degenerate bifurcation point P 1 , via which the BHom bifurcation terminates and the LPC bifurcation emerges, is responsible for the spiking transition from type I to type II. In addition, the I Na,p +I K model presents bifurcations in two-parameter space more complex than those in the ML model, H-H model, and many other neuronal model with highdimension and multiple variables [13,[54][55][56][57][58][66][67][68][69][70].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Recently, I h current induces SNIC changed to Hopf bifurcation, which further implies that the PIR spike induced by I h current is related to the Hopf bifurcation [57]. More recently, in a three-dimensional neuronal model with I h current, the PIR spike appears near SNIC because the threshold surface changes for stronger I h current [58]. However, up to now, no PIR spike is identified to appear near SNIC in a two-dimensional model.…”

Section: Introductionmentioning

confidence: 93%

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Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Wang

et al. 2021

Preprint

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Neuron exhibits nonlinear dynamics such as excitability transition and post-inhibitory rebound (PIR) spike related to bifurcations, which are associated with information processing, locomotor modulation, or brain disease. PIR spike is evoked by inhibitory stimulation instead of excitatory stimulation, which presents a challenge to the threshold concept. In the present paper, 7 codimension-2 or degenerate bifurcations related to 10 codimension-1 bifurcations are acquired in a neuronal model, which presents the bifurcations underlying the excitability transition and PIR spike. Type I excitability corresponds to saddle-node bifurcation on an invariant cycle (SNIC) bifurcation, and type II excitability to saddle-node (SN) bifurcation or sub-critical Hopf (SubH) bifurcation or sup-critical Hopf (SupH) bifurcation. The excitability transition from type I to II corresponds to the codimension-2 bifurcation, Saddle-Node Homoclinic orbit (SNHO) bifurcation, via which SNIC bifurcation terminates and meanwhile big homoclinic orbit (BHom) bifurcation and SN bifurcation emerge. A degenerate bifurcation via which BHom bifurcation terminates and fold limit cycle (LPC) bifurcation emerges is responsible for spiking transition from type I to II, and the roles of other codimension-2 bifurcations (Cusp, Bogdanov-Takens, and Bautin) are discussed. In addition, different from the widely accepted viewpoint that PIR spike is mainly evoked near Hopf bifurcation rather than SNIC bifurcation, PIR spike is identified to be induced near SNIC or BHom or LPC bifurcations, and threshold curves resemble that of Hopf bifurcation. The complex bifurcations present comprehensive and deep understandings of excitability transition and PIR spike, which are helpful for the modulation to neural firing activities and physiological functions.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Wang

et al. 2021

Preprint

Self Cite

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“…This phenomenon is hard to be reproduced in climatic research but can be confirmed by various artificially designed experiments including crayfish ( Douglass et al, 1993 ), shark ( Braun et al, 1994 ), rat ( Collins et al, 1996 ), cricket ( Levin and Miller, 1996 ), optical material ( Dylov and Fleischer, 2010 ) and human ( Winterer et al, 1999 ; Zeng et al, 2000 ). The experiments successfully revealed that noise can play a potential but positive role in neural information processing, and further encouraged extensive theoretical progress, such as noise enhanced weak signal detection ( Kang et al, 2005 ; Sun et al, 2019 ; Kang et al, 2022 ), noise facilitated information coding ( Du et al, 2010 ; Nakamura and Tateno, 2019 ; Guan et al, 2021 ) and noise enhanced chaos control ( Lei et al, 2017 ). Nowadays how to utilize noise for developing novel brain-like algorithms, such as visual perception ( Simonotto et al, 1997 ; Fu et al, 2020 ; Xu et al, 2022 ) and epileptic diagnosis preprocessing ( Shi et al, 2023 ), has attracted more and more interest in the current age of artificial intelligence.…”

Section: Introductionmentioning

confidence: 88%

Mutual information measure of visual perception based on noisy spiking neural networks

Xu,

Zhai,

Kang

2023

Front. Neurosci.

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Note that images of low-illumination are weak aperiodic signals, while mutual information can be used as an effective measure for the shared information between the input stimulus and the output response of nonlinear systems, thus it is possible to develop novel visual perception algorithm based on the principle of aperiodic stochastic resonance within the frame of information theory. To confirm this, we reveal this phenomenon using the integrate-and-fire neural networks of neurons with noisy binary random signal as input first. And then, we propose an improved visual perception algorithm with the image mutual information as assessment index. The numerical experiences show that the target image can be picked up with more easiness by the maximal mutual information than by the minimum of natural image quality evaluation (NIQE), which is one of the most frequently used indexes. Moreover, the advantage of choosing quantile as spike threshold has also been confirmed. The improvement of this research should provide large convenience for potential applications including video tracking in environments of low illumination.

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“…The study to these problems can enable us to further understand the mechanisms of different rhythm patterns more deeply and comprehensively, which is helpful for the application the antiphase bursting in motion control of robot and so on. In addition, the I h is a special current which can modulate the threshold (Guan et al, 2019) and resonances (Guan et al, 2020(Guan et al, , 2021 and is associated with the dendritic integration, synaptic transmission, motor learning, pacemaker function, and pathologies (Robinson and Siegelbaum, 2003;Biel et al, 2009;Wahl-Schott and Biel, 2009), which should be further studied in future.…”

Section: Silence Of the Antiphase Bursting Is Related To The Unstable...mentioning

confidence: 99%

Dynamics of antiphase bursting modulated by the inhibitory synaptic and hyperpolarization-activated cation currents

Guan,

Gu,

Zhang

2024

Front. Comput. Neurosci.

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Antiphase bursting related to the rhythmic motor behavior exhibits complex dynamics modulated by the inhibitory synaptic current (Isyn), especially in the presence of the hyperpolarization-activated cation current (Ih). In the present paper, the dynamics of antiphase bursting modulated by the Ih and Isyn is studied in three aspects with a theoretical model. Firstly, the Isyn and the slow Ih with strong strength are the identified to be the necessary conditions for the antiphase bursting. The dependence of the antiphase bursting on the two currents is different for low (escape mode) and high (release mode) threshold voltages (Vth) of the inhibitory synapse. Secondly, more detailed co-regulations of the two currents to induce opposite changes of the bursting period are obtained. For the escape mode, increase of the Ih induces elevated membrane potential of the silence inhibited by a strong Isyn and shortened silence duration to go beyond Vth, resulting in reduced bursting period. For the release mode, increase of the Ih induces elevated tough value of the former part of the burst modulated by a nearly zero Isyn and lengthen burst duration to fall below Vth, resulting in prolonged bursting period. Finally, the fast-slow dynamics of the antiphase bursting are acquired. Using one-and two-parameter bifurcations of the fast subsystem of a single neuron, the burst of the antiphase bursting is related to the stable limit cycle, and the silence modulated by a strong Isyn to the stable equilibrium to a certain extent. The Ih mainly modulates the dynamics within the burst and quiescent state. Furthermore, with the fast subsystem of the coupled neurons, the silence is associated with the unstable equilibrium point. The results present theoretical explanations to the changes in the bursting period and fast-slow dynamics of the antiphase bursting modulated by the Isyn and Ih, which is helpful for understanding the antiphase bursting and modulating rhythmic motor patterns.

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Dynamics of subthreshold and suprathreshold resonance modulated by hyperpolarization-activated cation current in a bursting neuron

Cited by 15 publications

References 64 publications

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Mutual information measure of visual perception based on noisy spiking neural networks

Dynamics of antiphase bursting modulated by the inhibitory synaptic and hyperpolarization-activated cation currents

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