Aspects of Signal Processing in Noisy Neurons

Abstract

It has become clear in recent years that stochastic effects, commonly known as noise, do not necessarily impede signal processing, but may actually serve to enhance it. The effect is known as stochastic resonance. It is plausible to assume that evolution has found ways to utilize this phenomenon to otpimize information processing in the nervous system. This dissertation investigated whether the coding of periodic signals in neurons is enhanced by the background noise ubiquitous in the nervous system. The study focuses on the leaky integrate-and-fire model neuron. The investigation is based on the theory of point processes. The distribution of intervals between any two successive spikes emitted by the neuron is determined numerically from an integral-equation ansatz, while the temporal order of spike trains relative to the input signal is characterized by a Markov chain. In addition, the validity of some approximations to the interspike-interval distribution is tested, permitting for more detailed analytic investigations. The central result of this dissertation is that the model neuron exhibits two kinds of stochastic resonance: on the one hand classical stochastic resonance, i.e. an optimal signal-to-noise ratio of the evoked spike train at a particular input noise amplitude. Second, a resonance with respect to the frequency of the input signal or stimulus. Stimuli within a certain frequency range are coded into spike trains with precise temporal structure, while stimuli outside the preferred range elicit more homogenous trains. This twofold resonance is termed stochastic double resonance. This effect is explained in terms of elementary mechanisms and its dependency on stimulus properties is explored in detail. It is shown that the response of the neuron follows simple scaling laws. In particular, the optimal, scaled noise amplitude is found to be a universal parameter of the model independent of the stimulus. The optimal stimulus frequency, in contrast, depends linearly on the stimulus amplitude with a constant of proportionality depending on the DC component of the stimulus (base current). Large base currents practically decouple frequency and amplitude will be coded in temporally well-structured spike trains, while small base currents permit to select the optimal frequency band by variation of the stimulus amplitude.