Neural encoding in invertebrate neurons

Stochastic resonance in two simple compare-and-fire models

Two neural models are analysed and shown to exhibit the stochastic resonance effect. Namely, they respond to an underthreshold sinusoidal signal with an output signal whose signal-to-noise ratio (SNR) firstly increases then decreases as the intensity of noise affecting the system increases. The resonance curves are determined, analytically for the first and simplest model and by a synthetic method for the second one, and the respective resonant behaviours are illustrated and interpreted.

Stochastic resonance in a sinusoidally forced LIF model with noisy threshold

In this report, the LIF neural model driven by underthreshold sinusoidal signals but with a gaussian-distributed noise on the threshold, is approximated by suitably defining an instantaneous firing (or escape) rate, which depends only on the momentary value of the voltage variable. This allows us to obtain, by analytically solving the relevant equations, the main statistical functions describing the "firing activity"; namely, the probability density function of firing phases and that of interspike intervals. From these functions two quantities can be derived, whose dependence on the noise intensity allows the Stochastic Resonance (SR) to be demonstrated. Besides the "regular" SR, the analysed system was found to produce, either for low frequencies and large amplitudes of modulation or for high modulation frequencies, resonance curves displaying two peaks. This bimodal feature of the resonance curves is accounted for on the basis of phase locked firing patterns.

Dynamics of the neural discharge in snail neurons

Spike trains recorded under weak sinusoidal driving from central neurons of Lymnaea stagnalis appear quite irregular and envisage the possibility of an underlying chaotic process. Therefore, the sequences of interspike intervals are analyzed in the framework of non-linear dynamics. Since, for several reasons, these sequences are rather short, the analysis is performed by using methods of non-linear forecasting. To reject the null hypothesis that the original time series is a realization of a linear stochastic process with the same autocorrelation function, the results obtained on the original data are compared with those from surrogate data sets. Some 'non-linear' predictability occurs only in narrow regions of the space of stimulus parameters and the frequency of perturbation is critical in determining it. Moreover, it is shown that such behavior can be qualitatively mimicked by the FitzHugh-Nagumo model driven by a weak sinusoidal signal plus noise. It is argued that the narrowness of the non-linear predictability regions renders quite unlikely the detection of deterministic dynamics in the activity of these neurons.