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Neuronal spike-train responses in the presence of threshold noise

Coombes, Stephen; Thul, Ruediger; Laudanski, Jonathan; Palmer, Alan; Sumner, Chris

Authors

Ruediger Thul ruediger.thul@nottingham.ac.uk

Jonathan Laudanski jonathan.laudanski@googlemail.com

Alan Palmer alan@ihr.mrc.ac.uk

Chris Sumner Chris@ihr.mrc.ac.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.

Journal Article Type Article
Journal Frontiers in Life Science
Print ISSN 2155-3769
Electronic ISSN 2155-3769
Publisher Taylor & Francis
Peer Reviewed Peer Reviewed
Volume 5
Issue 3-4
Institution Citation Coombes, S., Thul, R., Laudanski, J., Palmer, A., & Sumner, C. (in press). Neuronal spike-train responses in the presence of threshold noise. Frontiers in Life Science, 5(3-4), doi:10.1080/21553769.2011.556016
DOI https://doi.org/10.1080/21553769.2011.556016
Keywords Integrate-and-fire, Arnol'd tongues, Stochastic mode-locking, Threshold noise, First passage times, Neural coding
Publisher URL http://dx.doi.org/10.1080/21553769.2011.556016
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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