Neuron dynamics in the presence of 1/f noise.

Interest in understanding the interplay between noise and the response of a nonlinear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in nonlinear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small steplike stimulus. For the perfect (nonleaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low-pass) filter function given by F(t,f)=sinc(2)(πft). This result elucidates the connection between low-frequency noise and disorder in neuron dynamics. Under 1/f noise, spike dynamics lacks a characteristic correlation time, inducing the leaky and nonleaky models, to exhibit nonergodic behavior and the Fano factor, increasing logarithmically as a function of time. We compare our results to experimental data of single neurons in vivo [Teich, Heneghan, Lowen, Ozaki, and Kaplan, J. Opt. Soc. Am. A 14, 529 (1997)] and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low-frequency noise, however, complicates the case for an information-coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.