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Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal signiﬁcance
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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. 923947. ISSN 08997667

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Official URL: http://dx.doi.org/10.1162/0899766053429444
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 currentbased models with an effective membrane time constant. The wellknown effectivetimeconstant approximation can therefore be identified as the leadingorder solution to the full conductancebased model. The higherorder modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shotnoise effects implying that analytical approaches such as the FokkerPlanck 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 nonGaussian effects. The effectivetimeconstant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.
[error in script] [error in script]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:  08997667 
Date:  April 2005 
Volume:  Vol.17 
Number:  No.4 
Page Range:  pp. 923947 
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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