Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin–Huxley systems

Schmid, Gerhard; Goychuk, Igor; Hänggi, Peter

doi:10.1088/1478-3975/3/4/002

Cited by 31 publications

(38 citation statements)

References 51 publications

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“…(7a) replaces Eq. (6) [22]. Remarkably, the nodal membrane size A, which is the same for all nodes, solely influences the intrinsic noise strength.…”

Section: Stochastic Generalization Of the Hodgkin-huxley Modelmentioning

confidence: 99%

Noise-assisted spike propagation in myelinated neurons

et al. 2009

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We consider noise-assisted spike propagation in myelinated axons within a multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal electric coupling, we show that (i) intrinsic noise removes the sharply defined threshold for spike propagation from node to node, and (ii) there exists an optimum number of ion channels which allows for the most efficient signal propagation and it corresponds to the actual physiological values.

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“…(7a) replaces Eq. (6) [22]. Remarkably, the nodal membrane size A, which is the same for all nodes, solely influences the intrinsic noise strength.…”

Section: Stochastic Generalization Of the Hodgkin-huxley Modelmentioning

confidence: 99%

Noise-assisted spike propagation in myelinated neurons

et al. 2009

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“…Spiral waves might serve as emergent population pacemakers, generating periodic activity in non-oscillatory networks without individual cellular pacemakers. The formation, death, and breakup of spiral waves in the mammalian cortex can be simulated using regular and/or small-world networks [8][9][10].In networks using Hodgkin-Huxley model neurons [20], the effects of channel noise [21,22] on spiral waves needs to be studied in detail.Normal signal propagation between neurons in networks with different topologies deeply depends on the collective behavior of neurons. Abnormalities of neurons in one domain can destroy the normal communication between neurons, and neurological disorders can occur when the normal electrical activity of neurons is violated.…”

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confidence: 99%

“…In networks using Hodgkin-Huxley model neurons [20], the effects of channel noise [21,22] on spiral waves needs to be studied in detail.…”

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confidence: 99%

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

Huang

et al. 2012

Chin. Sci. Bull.

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The breakup of a spiral wave by blockade of sodium and potassium channels in a small-world network of Hodgkin-Huxley neurons is investigated in detail. The influence of ion channel block in poisoned excitable membrane patches of a certain size is measured, by varying channel noise and channel densities resulting from the change in conductance. For example, tetraethylammonium is known to cause a block (poisoning) of potassium channels, while tetrodotoxin blocks sodium channels. We observed the occurrence of spiral waves, which are ordered waves believed to play an important role in facilitating the propagation of electric signals across quiescent regions of the brain. In this paper, the effect of channel block was measured by the factors x K and x Na , which represent the ratios of unblocked, or active, ion channels, to the overall number of potassium or sodium ion channels, respectively. To quantify these observations, we use a simple but robust synchronization measure, which succinctly captures the transition from spiral waves to other collective states, such as broken segments resulting from the breakup of the spiral wave. The critical thresholds of channel block can be inferred from the abrupt changes occurring in plots of the synchronization measure against different values of x K and x Na . Notably, small synchronization factors can be tightly associated with states where the formation of spiral waves is robust to mild channel block. A spiral wave is a characteristic spatiotemporal pattern that is often observed in excitable media [1][2][3][4][5][6][7][8][9][10]. The formation and propagation of spiral waves in reaction-diffusion systems have been studied extensively [11][12][13][14][15][16], and some effective schemes have been used to remove spiral waves and prevent ventricular fibrillation [17]. Stable rotating spiral waves have been observed in rat neocortical slices visualized by voltage-sensitive dye imaging [18,19]. Spiral waves might serve as emergent population pacemakers, generating periodic activity in non-oscillatory networks without individual cellular pacemakers. The formation, death, and breakup of spiral waves in the mammalian cortex can be simulated using regular and/or small-world networks [8][9][10].In networks using Hodgkin-Huxley model neurons [20], the effects of channel noise [21,22] on spiral waves needs to be studied in detail.Normal signal propagation between neurons in networks with different topologies deeply depends on the collective behavior of neurons. Abnormalities of neurons in one domain can destroy the normal communication between neurons, and neurological disorders can occur when the normal electrical activity of neurons is violated. The response of neurons to external stimuli (drugs or electrical forcing) is often a result of the collective behaviors of all the neurons in one or more domains. It is reliable to study the collective electrical activities of neurons in functional domains using complex network schemes. Most previous schemes have been proposed to remove spira...

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“…It is better to study spiral wave dynamics in networks of Hodgkin-Huxley (H-H) neurons than in networks of Hindmarsh-Rose (H-R) neurons [4,5] because the H-R neuron model is a simplified version of the realistic H-H model. Channel noise can change the dynamics of H-H neurons greatly [31,32]. White et al [31] pointed out that the probabilistic gating of voltage-dependent ion channels is a source of electrical 'channel noise' in neurons.…”

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confidence: 99%

“…White et al [31] pointed out that the probabilistic gating of voltage-dependent ion channels is a source of electrical 'channel noise' in neurons. Schmid et al [32] reported the capacitance fluctuations reducing channel noise in stochastic H-H systems. Fox et al [33] presented the autocorrelation functions of channel noise to estimate the effect of channel noise.…”

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confidence: 99%

Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons

Huang

et al. 2011

Chin. Sci. Bull.

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The phase transition of spiral waves in networks of Hodgkin-Huxley neurons induced by channel noise is investigated in detail. All neurons in the networks are coupled with small-world connections, and the results are compared with the case for regular networks, in which all neurons are completely coupled with nearest-neighbor connections. A statistical variable is defined to study the collective behavior and phase transition of the spiral wave due to the channel noise and topology of the network. The effect of small-world connection networks is described by local regular networks and long-range connection with certain probability p. The numerical results confirm that (1) a stable rotating spiral wave can be developed and maintain robust with low p, where the breakup of the spiral wave and turbulence result from increasing the probability p to a certain threshold; (2) appropriate intensity of the optimized channel noise can develop a spiral wave among turbulent states in small-world connection networks of H-H neurons; and (3) regular connection networks are more robust to channel noise than small-world connection networks. A spiral wave in a small-world network encounters instability more easily as the membrane temperature is increased to a certain high threshold.breakup, channel noise, factor of synchronization, probability of long-range connection Citation:Ma J, Wu Y, Ying H P, et al. Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons.

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Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin–Huxley systems

Cited by 31 publications

References 51 publications

Noise-assisted spike propagation in myelinated neurons

Noise-assisted spike propagation in myelinated neurons

Detecting the breakup of spiral waves in small-world networks of neurons due to channel block

Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons

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