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- T. Hoch, G. Wenning, and
K. Obermayer. Optimal Noise-Aided Signal Transmission through Populations
of Neurons.
.
Phys. Rev. E, 68:11911, 2003.
(FTP Gzipped PostScript, 12 pages, 128 kb)
Metabolic considerations and neurophysiological measurements
indicate that biological neural systems prefer information transmission via
many parallel low intensity channels, compared to few high intensity ones [S.
B. Laughlin et. al., Nature Neurosci., 1, 36 (1998)]. Furthermore, cortical
neurons are exposed to a considerable amount of synaptic background activity,
which increases the neurons conductance and leads to a fluctuating membrane
potential that on average, is close to the threshold [A. Destexhe and D.
Par?, J. Neurophysiol., 81, 1531 (1999)]. Recent studies have shown, that
noise can improve the transmission of subthreshold signals in populations of
neurons, e.g., if their response is pooled. In general, the optimal noise
level depends on the stimulus distribution and on the number of neurons in
the population. In this contribution we show that for a large enough number
of neurons the latter dependency becomes weak, such that the optimal noise
level becomes almost independent of the number of neurons in the population.
First we investigate a binary threshold model of neurons. We derive an
analytic expression for the optimal noise level at each single neuron, which
- for a large enough population size - depends only on quantities that are
locally available to a single neuron. Using numerical simulations, we then
verify the weak dependence of the optimal noise level on population size in a
more realistic framework using leaky integrate-and-fire as well as
Hodgkin-Huxley type model neurons. Next we construct a cost function, where
quality of information transmission is traded against its metabolic costs.
Again we find that - for subthreshold signals - there is an optimal noise
level which maximizes this cost. This noise level, however, is almost
independent of the number of neurons, even for small population sizes, as
numerical simulations using the Hodgkin-Huxley model show. Since the
dependence of the optimal noise level on population size is weak for large
enough populations, local neural adaptation is sufficient to adjust the level
of noise to its optimal value.
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