Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels

Fox, Ronald F.; Lu, Yannan

doi:10.1103/physreve.49.3421

Cited by 274 publications

(377 citation statements)

References 11 publications

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“…To account for the effect of channel noise, we use a generalization of the model introduced originally by Fox and Lu [28] which presents a stochastic generalization of the Hodgkin-Huxley equations (1-4). Due to the Kramers-Moyal expansion of the corresponding master equations, the dynamics of the gating variables is given by the following Langevin equation, interpreted here in the stochastic interpretation of Itô [29][30][31], reading…”

Section: Stochastic Generalization Of Hodgkin-huxley Modelmentioning

confidence: 99%

Intrinsic coherence resonance in excitable membrane patches

Schmid¹,

Hänggi²

2007

Mathematical Biosciences

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The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. There exists an optimal size of the membrane patch for which the internal noise alone can cause a nearly regular spontaneous generation of action potentials. We consider the influence of intrinsic channel noise in presence of a constant and an oscillatory current driving for both, the mean interspike interval and the phenomenon of coherence resonance for neuronal spiking. Given small membrane patches, implying that channel noise dominates the excitable dynamics, we find the phenomenon of intrinsic coherence resonance. In this case, the relatively regular spiking behavior becomes essentially independent of an applied stimulus. We observed, however, the occurrence of a skipping of supra-threshold input events due to channel noise for intermediate patch sizes. This effect consequently reduces the overall coherence of the spiking.

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Section: Stochastic Generalization Of Hodgkin-huxley Modelmentioning

confidence: 99%

Intrinsic coherence resonance in excitable membrane patches

Schmid¹,

Hänggi²

2007

Mathematical Biosciences

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“…The number of open gates undergoes a birth-and-death-like process. The corresponding master equation can readily be written down [10]. The use of a Kramers-Moyal expansion in that equation results in a corresponding Fokker-Planck equation which provides a diffusional approximation to the discrete dynamics.…”

Section: A Stochastic Generalization Of the Hodgkin-huxley Modelmentioning

confidence: 99%

“…Therefore, the strength of the channel noise is mainly determined by the number of ion channels participating in the generation of action potentials. Channel noise impacts, for example, such features as the threshold to spiking and the spiking rate itself [6][7][8][9][10][11][12], the anomalous noiseassisted enhancement of transduction of external signals, i.e. the phenomenon of stochastic resonance [13][14][15][16][17][18][19][20][21][22][23][24], and the efficiency for synchronization [25].…”

Section: Introductionmentioning

confidence: 99%

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

2006

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Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane, but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential, the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley-like modeling takes into account both the channel noise-i.e. the fluctuations of the number of open ion channels-and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of a variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.

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“…Fox and Lu developed a stochastic extension [4] of the Hodgkin-Huxley model [1] which accounts for channel noise. The origin of the channel noise [3] is basically due to uctuations of the number of open ion channels around the corresponding mean values.…”

Section: A Stochastic Hodgkin-huxley Modelmentioning

confidence: 99%

“…But since Lecar and Nossal [2], it is taken for granted that the randomness of the ion channel gating causes threshold uctuations in neurons. Therefore, channel noise which stems from the stochastic nature of the ion channel dynamics cannot be disregarded [3]; it impacts, e.g., features such as the threshold to spiking, the spiking rate itself [4][5][6][7] and the e ciency for synchronization [8]. The strength of the channel noise is mainly determined by the number of ion channels participating in the generation of action potentials.…”

Section: Introductionmentioning

confidence: 99%

Controlling the spiking activity in excitable membranes via poisoning

Schmid

Goychuk

Hänggi

2004

Physica A: Statistical Mechanics and its Applications

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The in uence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to a ect the collective properties of the whole ion channel cluster. There exists an optimal size of the membrane patch for which, solely, the internal noise causes a most regular spontaneous generation of action potentials. In addition to the variation of the size of ion channel clusters, living organisms may adopt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. In our model, we selectively control via poisoning the densities of speciÿc, active ion channels. Interestingly enough, by such poisoning of some of the potassium, or the sodium ion channels, respectively, it is possible to either increase, or decrease the regularity of the spike train.

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Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels

Cited by 274 publications

References 11 publications

Intrinsic coherence resonance in excitable membrane patches

Intrinsic coherence resonance in excitable membrane patches

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

Controlling the spiking activity in excitable membranes via poisoning

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