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
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