Richardson, Magnus J. E. and Gerstner, Wulfram (2005) Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance. Neural Computation, Vol.17 (No.4). pp. 923-947. ISSN 0899-7667

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Abstract

The subthresholdmembranevoltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductancebased synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Item Type:	Journal Item
Subjects:	Q Science > QP Physiology
Divisions:	Faculty of Science > Centre for Systems Biology
Library of Congress Subject Headings (LCSH):	Neurons -- Mathematical models, Neural transmission -- Mathematical models, Cerebral cortex, Cell membranes
Journal or Publication Title:	Neural Computation
Publisher:	MIT Press
ISSN:	0899-7667
Date:	April 2005
Volume:	Vol.17
Number:	No.4
Page Range:	pp. 923-947
Identification Number:	10.1162/0899766053429444
Status:	Peer Reviewed
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/34561

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