Optimal noise-aided signal transmission through populations of neurons

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 , 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. Pare, 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.