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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

A-C. ISI scattergrams of the responses of a VCN chopper unit to amplitude modulated tones. The tone was 3 s long, with a frequency the same as the characteristic frequency of the unit, 50 dB above the CF threshold. AM depth was 100% and frequency was as indicated. D-F. The responses of a stochastic-threshold IF model fitted to the data. The model parameters were: sinuisodal input: a = 0.7, I0 = 1.5 mV, threshold noise: σ = 2.7, η = 0.75 ms, IF parameters: τ = 3.18 ms, VL = VR = − 60 mV, Vth = − 42 mV. G. An example of the evolution of the membrane potential of the model (blue) for the 50 Hz modulation rate, the stochastic threshold (green) and the modulated input on an arbitrary scale.
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Figure 9: A-C. ISI scattergrams of the responses of a VCN chopper unit to amplitude modulated tones. The tone was 3 s long, with a frequency the same as the characteristic frequency of the unit, 50 dB above the CF threshold. AM depth was 100% and frequency was as indicated. D-F. The responses of a stochastic-threshold IF model fitted to the data. The model parameters were: sinuisodal input: a = 0.7, I0 = 1.5 mV, threshold noise: σ = 2.7, η = 0.75 ms, IF parameters: τ = 3.18 ms, VL = VR = − 60 mV, Vth = − 42 mV. G. An example of the evolution of the membrane potential of the model (blue) for the 50 Hz modulation rate, the stochastic threshold (green) and the modulated input on an arbitrary scale.


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

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

A-C. ISI scattergrams of the responses of a VCN chopper unit to amplitude modulated tones. The tone was 3 s long, with a frequency the same as the characteristic frequency of the unit, 50 dB above the CF threshold. AM depth was 100% and frequency was as indicated. D-F. The responses of a stochastic-threshold IF model fitted to the data. The model parameters were: sinuisodal input: a = 0.7, I0 = 1.5 mV, threshold noise: σ = 2.7, η = 0.75 ms, IF parameters: τ = 3.18 ms, VL = VR = − 60 mV, Vth = − 42 mV. G. An example of the evolution of the membrane potential of the model (blue) for the 50 Hz modulation rate, the stochastic threshold (green) and the modulated input on an arbitrary scale.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 9: A-C. ISI scattergrams of the responses of a VCN chopper unit to amplitude modulated tones. The tone was 3 s long, with a frequency the same as the characteristic frequency of the unit, 50 dB above the CF threshold. AM depth was 100% and frequency was as indicated. D-F. The responses of a stochastic-threshold IF model fitted to the data. The model parameters were: sinuisodal input: a = 0.7, I0 = 1.5 mV, threshold noise: σ = 2.7, η = 0.75 ms, IF parameters: τ = 3.18 ms, VL = VR = − 60 mV, Vth = − 42 mV. G. An example of the evolution of the membrane potential of the model (blue) for the 50 Hz modulation rate, the stochastic threshold (green) and the modulated input on an arbitrary scale.
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