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Synaptic shot noise and conductance fluctuations affect the\ud membrane voltage with equal significance

By Magnus J. E. Richardson and Wulfram Gerstner

Abstract

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

Topics: QP
Publisher: MIT Press
Year: 2005
OAI identifier: oai:wrap.warwick.ac.uk:34561

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