There is a theoretical upper limit of how fast a neuron can fire, based on the duration of its spike and refractory period. Therefore, under certain conditions, its firing rate might fit a Gaussian distribution. One possible situation would be the distribution of firing rate responses to a preferred stimulus. Has there been a treatment of that question in the literature in relation to stimulus selectivity?
Hi,
There is huge literature about Gaussian tuning curves in response to auditory and visual stimuli, early described by Hubel and Wiesel in cat visual cortex.
Hole it helps!!
Motoneuron firing in higher frequency range has normal distribution. See classical paper: Person RS, Kudina LP. Discharge frequency and discharge pattern of human motor units during voluntary contraction of muscle. Electroencephalogr Clin Neurophysiol 1972; 32:471–83.
My impression is that whenever firing rates are high you get a more or less symmetric firing rate distribution than can be approximated by a Gaussian (though small deviation from normality such as the presence of heavy-tails may nevertheless be conceptually important). For example, given the standard model of neural firing rates following Poisson statistics, the Poisson distribution is well approximated by a Gaussian distribution for firing rates of more than around 10 spikes/sec. For low firing rates the probability distribution becomes skewed to the right, because firing rates can't drop below zero. In that case the Gaussian distribution becomes a poor approximation. Informally I think of zero spikes/sec as forming an impenetrable lower boundary, and the left tail of the distribution getting squashed against that boundary as mean firing rate drops, producing a very skewed, non-Gaussian distribution.
I have published a paper on probability distributions in relation to stimulus selectivity in monkey inferotemporal cortex, though I'm not sure if this is what you have in mind:
Lehky SR, Kiani R, Esteky H, Tanaka K (2011) Statistics of visual responses in primate inferotemporal cortex to object stimuli. J Neurophysiol. 2011 Sep;106:1097-117
I don't see why having an upper limit to firing rates caused by a refractory period would in itself necessarily lead to a Gaussian firing rate distribution.
Dear all,
Just one question: when you talk about "firing rate distribution", do you mean "interspike interval length distribution"? If that be the case, I would argue that Gaussian distributions have non-zero probability from minus infinity to any point on the real line, and that makes me skeptical about using gaussians: I would, at least, expect a lower bound of zero for any distribution modelling time interval lengths.
What would you argue in favor of Gaussians in this context?
Cheers,
Fernando
I was referring to firing rates, not interspike intervals. Thank you both for your answers and for that useful reference. An upper limit in firing rates would stop a distribution from being Poisson, since rates cannot increase beyond a certain value. That upper limit by itself would not produce a Gaussian distribution but it would tend to favour a Gaussian-like distribution over a Poisson like distribution, once the distribution moved away from 0,
Presumably the distribution of responses to non effective stimuli would be gamma or Poisson like, the distribution of responses to highly effective stimuli would be affected by the upper limit and would look like their mirror images, while responses to intermediately effective stimuli with a rate a bit over 10 spikes/sec would tend to be approximated by a Gaussian distribution. Hopefully someone will come up with more formal concepts at some point.
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