Neural Coherence and Stochastic Resonance

Abstract

This chapter concerns the influence of noise and periodic rhythms on the firing patterns of neurons in their subthreshold regime. Such a regime conceals many computations that lead to successive decisions to fire or not fire, and noise and rhythms are important components of these decisions. We first consider a TypeII neuron model, the FitzHugh-Nagumo model, characterized by a resonant frequency. In the subthreshold regime, noise induces firings with a regularity that increases with noise intensity. At a certain finite noise level, the regularity may be maximized, but this depends on the numerical implementation of an absolute refractory period. We discuss measures of this coherence resonance based on the coefficient of variation (CV) of interspike intervals and spike train power spectra. We then characterize its phase locking to periodic input, and how this locking is modified by noise. This lays the foundation for understanding how noise can express subthreshold signals in the spike train. We discuss measures and qualitative features of this stochastic resonance across all time-scales of periodic forcing. We show how the resonance relates to firing once per forcing cycle, on average, or submultiples thereof at higher forcing frequencies where refractory effects come into play. For slow forcing the optimal noise is independent of forcing period. We then discuss coherence resonance and stochastic resonance in the quadratic integrate-and-fire model of TypeI dynamics. The presence of a full coherence resonance depends on the interpretation of the model, particularly the boundaries for firing and reset. Our study is motivated by the observation of randomly phase locked firing activity in a large number of neurons, especially those involved in transducing physical stimuli such as temperature, sound, pressure, and electric fields, but also in central neurons involved in the generation of various rhythms.