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Neuronal spike-train responses in the presence of threshold noise.

Coombes S, Thul R, Laudanski J, Palmer AR, Sumner CJ - Front Life Sci (2012)

Bottom Line: We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times.This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure.An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

View Article: PubMed Central - PubMed

Affiliation: Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.

ABSTRACT

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent channel fluctuations or the stochastic nature of neurotransmitter release. Here we propose an alternative approach using a simple leaky integrate-and-fire model with a noisy threshold. Initially, we develop a mathematical treatment of the neuronal response to periodic forcing using tools from linear response theory and use this to highlight how a noisy threshold can enhance downstream signal reconstruction. We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times. This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure. An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

No MeSH data available.


Related in: MedlinePlus

The probability of firing in a model with Gaussian threshold noise. Here Vth = −40 mV and σ = 4 mV−1 (black), σ = 3 mV−1 (red), σ = 2 mV−1 (green), σ = 1 mV−1 (blue) and σ = 0.5 mV−1 (magenta).
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Figure 1: The probability of firing in a model with Gaussian threshold noise. Here Vth = −40 mV and σ = 4 mV−1 (black), σ = 3 mV−1 (red), σ = 2 mV−1 (green), σ = 1 mV−1 (blue) and σ = 0.5 mV−1 (magenta).


Neuronal spike-train responses in the presence of threshold noise.

Coombes S, Thul R, Laudanski J, Palmer AR, Sumner CJ - Front Life Sci (2012)

The probability of firing in a model with Gaussian threshold noise. Here Vth = −40 mV and σ = 4 mV−1 (black), σ = 3 mV−1 (red), σ = 2 mV−1 (green), σ = 1 mV−1 (blue) and σ = 0.5 mV−1 (magenta).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525809&req=5

Figure 1: The probability of firing in a model with Gaussian threshold noise. Here Vth = −40 mV and σ = 4 mV−1 (black), σ = 3 mV−1 (red), σ = 2 mV−1 (green), σ = 1 mV−1 (blue) and σ = 0.5 mV−1 (magenta).
Bottom Line: We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times.This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure.An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

View Article: PubMed Central - PubMed

Affiliation: Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.

ABSTRACT

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent channel fluctuations or the stochastic nature of neurotransmitter release. Here we propose an alternative approach using a simple leaky integrate-and-fire model with a noisy threshold. Initially, we develop a mathematical treatment of the neuronal response to periodic forcing using tools from linear response theory and use this to highlight how a noisy threshold can enhance downstream signal reconstruction. We further develop a more general framework for understanding the responses to large amplitude forcing based on a calculation of first passage times. This is ideally suited to understanding stochastic mode-locking, for which we numerically determine the Arnol'd tongue structure. An examination of data from regularly firing stellate neurons within the ventral cochlear nucleus, responding to sinusoidally amplitude modulated pure tones, shows tongue structures consistent with these predictions and highlights that stochastic, as opposed to deterministic, mode-locking is utilised at the level of the single stellate cell to faithfully encode periodic stimuli.

No MeSH data available.


Related in: MedlinePlus