Stochastic resonance in a model neuron with reset

Abstract

The response of a noisy integrate-and-fire neuron with reset to periodic input is investigated. We numerically obtain the first-passage-time density of the pertaining Ornstein-Uhlenbeck process and show how the power spectral density of the resulting spike train can be determined via Fourier transform. The neuron's output clearly exhibits stochastic resonance.

Statistical Models of Spike Trains

“…However, the stochastic calculus leads directly to partial differential equation (Risken, 1996;Paninski et al, 2004c) or integral equation (Siegert, 1951;Buoncore et al, 1987;Plesser and Tanaka, 1997;Burkitt and Clark, 1999;DiNardo et al, 2001;Paninski et al, 2007a;Mullowney and Iyengar, 2007) methods for computing the likelihood. For example, it is well-known (Tuckwell, 1989) that the probability density of the next spike satisfies…”

“…Alternately, p(τ |θ) solves a number of integral equations of the form Siegert, 1951;Ricciardi, 1977;Plesser and Tanaka, 1997;Burkitt and Clark, 1999;DiNardo et al, 2001;Paninski et al, 2007a;Mullowney and Iyengar, 2007), where the kernel function K(τ, t) and the left-hand-side f (t) may be computed as simple functions of the model parameters θ. In the case of constant current and conductance (I(t) = I, g(t) = g), this integral equation may be solved efficiently by Laplace transform techniques (Mullowney and Iyengar, 2007); more generally, the equation may be solved by numerical integration methods (Plesser and Tanaka, 1997;DiNardo et al, 2001) or by direct matrix inversion methods (Paninski et al, 2007a) (the latter methods also lead to simple formulas for the derivative of the likelihood with respect to the model parameters; this gradient information is useful for optimization of the model parameters, and for assessing the accuracy of the parameter estimates).…”

“…In the case of constant current and conductance (I(t) = I, g(t) = g), this integral equation may be solved efficiently by Laplace transform techniques (Mullowney and Iyengar, 2007); more generally, the equation may be solved by numerical integration methods (Plesser and Tanaka, 1997;DiNardo et al, 2001) or by direct matrix inversion methods (Paninski et al, 2007a) (the latter methods also lead to simple formulas for the derivative of the likelihood with respect to the model parameters; this gradient information is useful for optimization of the model parameters, and for assessing the accuracy of the parameter estimates). Thus, to summarize, stochastic process methods may be used to derive efficient schemes for computing the likelihood in this model.…”

Harmony perception and regularity of spike trains in a simple auditory model

“…For the Ornstein-Uhlenbeck neuronal model, the ISID was obtained analytically with different approaches in Refs. [33,34]. This distribution, which coincides with the first passage time probability distribution related to the firing event of sensory neurons, is our starting point to obtain the ISID at the output of the interneuron.…”

Transient information flow in a network of excitatory and inhibitory model neurons: Role of noise and signal autocorrelation

“…Such an effect is seen when the response of a system to a drive depends non-monotonically on noise, with an optimum at a moderate, non-zero, noise level. There are many pointers in the literature to physical evidences of stochastic resonance in physical systems [69,11,23,24,47,71,70], and in models of neurons [8,42,55,54]. In living systems stochastic resonance has been reported in crayfish mechanoreceptors [16], the cricket cercal sensory system [40], neural slices [27], hippocampus [72], and the cortex [48].…”