Models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish

Abstract

Two types of minimal models were used to study stochastic oscillations in sensory receptors composed of two coupled oscillators, as in the electroreceptors of paddlefish. They have populations of cells in sensory epithelia undergoing approximately 26 Hz oscillations. These are coupled unidirectionally via synaptic excitation to a few afferent neurons, each of whose terminal contains a 30-70 Hz oscillator, expressed as a dominant peak in the power spectra of spontaneous afferent firing, corresponding to the mean firing rate. The two distinct types of internal noisy oscillators result in stochastic biperiodic firing patterns of the primary afferent sensory neurons. However, the functions of the oscillations have remained elusive, motivating this study. The models we used here are based on the circle map, or on the Ermentraut-Koppell canonical phase (theta neuron) model. Parameters were chosen according to experimental data. We used the models to demonstrate that the presence of epithelial oscillations leads to extended negative correlations of afferent interspike intervals, and to show that the correlation structure depends crucially on the ratio of the afferent to epithelial oscillation frequencies, being most pronounced when this ratio is close to 2, as observed in experiments. Our studies of stochastic versions of these models are of general interest for a wide range of coupled excitable systems, especially for understanding the functional roles of noisy oscillations in auditory and other types of "hair cell-primary afferent" sensory receptors.