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Systematic analysis of the contributions of stochastic voltage gated channels to neuronal noise.

O'Donnell C, van Rossum MC - Front Comput Neurosci (2014)

Bottom Line: While this effect is well known, the impact of channel noise on single neuron dynamics remains poorly understood.Most results are based on numerical simulations.Here we describe a framework to calculate voltage noise directly from an arbitrary set of ion channel models, and discuss how this can be use to estimate spontaneous spike rates.

View Article: PubMed Central - PubMed

Affiliation: Computational Neurobiology Laboratory, Salk Institute for Biological Studies La Jolla, CA, USA ; School of Informatics, Institute for Adaptive and Neural Computation, University of Edinburgh Edinburgh, UK.

ABSTRACT
Electrical signaling in neurons is mediated by the opening and closing of large numbers of individual ion channels. The ion channels' state transitions are stochastic and introduce fluctuations in the macroscopic current through ion channel populations. This creates an unavoidable source of intrinsic electrical noise for the neuron, leading to fluctuations in the membrane potential and spontaneous spikes. While this effect is well known, the impact of channel noise on single neuron dynamics remains poorly understood. Most results are based on numerical simulations. There is no agreement, even in theoretical studies, on which ion channel type is the dominant noise source, nor how inclusion of additional ion channel types affects voltage noise. Here we describe a framework to calculate voltage noise directly from an arbitrary set of ion channel models, and discuss how this can be use to estimate spontaneous spike rates.

No MeSH data available.


Related in: MedlinePlus

Spontanous action potentials in the HH model driven with Gaussian noise with varying amplitude and correlation time. (A) The impedance factor z(τ) gives the voltage fluctuations resulting from a correlated noise current as a function of the noise correlation time. It is used to ensure the voltage variance is identical as the time constant of the noise is varied. Membrane area of 1000 μm2. (B) Spontaneous activity as a result of a Gaussian current noise, as a function of the correlation time of the noise. When the variance of the current is fixed, the resulting rates vary strongly depending on the correlation time (dashed curve). However, when the noise is calibrated to yield the same variance in the membrane voltage irrespective of the noise correlation time, the firing rate is much less variable even across six orders of magnitude (solid curve). (C) The firing rate vs. the impedance corrected current noise (expressed in σV) for various values of the noise time-constant. (D) The spontaneous firing rate vs. membrane area for K+ (red) and Na+ (blue) noise and their various approximations. Solid curve: full simulation, redrawn from Figure 1B. Thick dashed curve: approximation using Gaussian noise with identical variance and time-constant. Thin dashed curve: binomial approximation of the noise. In particular for Na+ noise the approximations yield rates that are substantially too low.
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Figure 5: Spontanous action potentials in the HH model driven with Gaussian noise with varying amplitude and correlation time. (A) The impedance factor z(τ) gives the voltage fluctuations resulting from a correlated noise current as a function of the noise correlation time. It is used to ensure the voltage variance is identical as the time constant of the noise is varied. Membrane area of 1000 μm2. (B) Spontaneous activity as a result of a Gaussian current noise, as a function of the correlation time of the noise. When the variance of the current is fixed, the resulting rates vary strongly depending on the correlation time (dashed curve). However, when the noise is calibrated to yield the same variance in the membrane voltage irrespective of the noise correlation time, the firing rate is much less variable even across six orders of magnitude (solid curve). (C) The firing rate vs. the impedance corrected current noise (expressed in σV) for various values of the noise time-constant. (D) The spontaneous firing rate vs. membrane area for K+ (red) and Na+ (blue) noise and their various approximations. Solid curve: full simulation, redrawn from Figure 1B. Thick dashed curve: approximation using Gaussian noise with identical variance and time-constant. Thin dashed curve: binomial approximation of the noise. In particular for Na+ noise the approximations yield rates that are substantially too low.

Mentions: The function z(τ) is an impedance that relates the voltage variance to the current variance of injected colored noise with time-constant τ. It is given by z2(τ) = ∫ SI(f)/Z(f)/2df, where is the power-spectrum of the noise current, and Z(f) the linearized impedance of the HH model. Its shape reflects the resonance in the impedance, Figure 5A. As a result of this impedance correction the membrane voltage variance in the limit of small fluctuations equals σ2V and is thus independent of τ.


Systematic analysis of the contributions of stochastic voltage gated channels to neuronal noise.

O'Donnell C, van Rossum MC - Front Comput Neurosci (2014)

Spontanous action potentials in the HH model driven with Gaussian noise with varying amplitude and correlation time. (A) The impedance factor z(τ) gives the voltage fluctuations resulting from a correlated noise current as a function of the noise correlation time. It is used to ensure the voltage variance is identical as the time constant of the noise is varied. Membrane area of 1000 μm2. (B) Spontaneous activity as a result of a Gaussian current noise, as a function of the correlation time of the noise. When the variance of the current is fixed, the resulting rates vary strongly depending on the correlation time (dashed curve). However, when the noise is calibrated to yield the same variance in the membrane voltage irrespective of the noise correlation time, the firing rate is much less variable even across six orders of magnitude (solid curve). (C) The firing rate vs. the impedance corrected current noise (expressed in σV) for various values of the noise time-constant. (D) The spontaneous firing rate vs. membrane area for K+ (red) and Na+ (blue) noise and their various approximations. Solid curve: full simulation, redrawn from Figure 1B. Thick dashed curve: approximation using Gaussian noise with identical variance and time-constant. Thin dashed curve: binomial approximation of the noise. In particular for Na+ noise the approximations yield rates that are substantially too low.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4199219&req=5

Figure 5: Spontanous action potentials in the HH model driven with Gaussian noise with varying amplitude and correlation time. (A) The impedance factor z(τ) gives the voltage fluctuations resulting from a correlated noise current as a function of the noise correlation time. It is used to ensure the voltage variance is identical as the time constant of the noise is varied. Membrane area of 1000 μm2. (B) Spontaneous activity as a result of a Gaussian current noise, as a function of the correlation time of the noise. When the variance of the current is fixed, the resulting rates vary strongly depending on the correlation time (dashed curve). However, when the noise is calibrated to yield the same variance in the membrane voltage irrespective of the noise correlation time, the firing rate is much less variable even across six orders of magnitude (solid curve). (C) The firing rate vs. the impedance corrected current noise (expressed in σV) for various values of the noise time-constant. (D) The spontaneous firing rate vs. membrane area for K+ (red) and Na+ (blue) noise and their various approximations. Solid curve: full simulation, redrawn from Figure 1B. Thick dashed curve: approximation using Gaussian noise with identical variance and time-constant. Thin dashed curve: binomial approximation of the noise. In particular for Na+ noise the approximations yield rates that are substantially too low.
Mentions: The function z(τ) is an impedance that relates the voltage variance to the current variance of injected colored noise with time-constant τ. It is given by z2(τ) = ∫ SI(f)/Z(f)/2df, where is the power-spectrum of the noise current, and Z(f) the linearized impedance of the HH model. Its shape reflects the resonance in the impedance, Figure 5A. As a result of this impedance correction the membrane voltage variance in the limit of small fluctuations equals σ2V and is thus independent of τ.

Bottom Line: While this effect is well known, the impact of channel noise on single neuron dynamics remains poorly understood.Most results are based on numerical simulations.Here we describe a framework to calculate voltage noise directly from an arbitrary set of ion channel models, and discuss how this can be use to estimate spontaneous spike rates.

View Article: PubMed Central - PubMed

Affiliation: Computational Neurobiology Laboratory, Salk Institute for Biological Studies La Jolla, CA, USA ; School of Informatics, Institute for Adaptive and Neural Computation, University of Edinburgh Edinburgh, UK.

ABSTRACT
Electrical signaling in neurons is mediated by the opening and closing of large numbers of individual ion channels. The ion channels' state transitions are stochastic and introduce fluctuations in the macroscopic current through ion channel populations. This creates an unavoidable source of intrinsic electrical noise for the neuron, leading to fluctuations in the membrane potential and spontaneous spikes. While this effect is well known, the impact of channel noise on single neuron dynamics remains poorly understood. Most results are based on numerical simulations. There is no agreement, even in theoretical studies, on which ion channel type is the dominant noise source, nor how inclusion of additional ion channel types affects voltage noise. Here we describe a framework to calculate voltage noise directly from an arbitrary set of ion channel models, and discuss how this can be use to estimate spontaneous spike rates.

No MeSH data available.


Related in: MedlinePlus