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Abstract
Stochastic signals with pronounced oscillatory components are frequently encountered in neural systems. Input currents to a neuron in the form of stochastic oscillations could be of exogenous origin, e.g. sensory input or synaptic input from a network rhythm. They shape spike firing statistics in a characteristic way, which we explore theoretically in this report. We consider a perfect integrate-and-fire neuron that is stimulated by a constant base current (to drive regular spontaneous firing), along with Gaussian narrow-band noise (a simple example of stochastic oscillations), and a broadband noise. We derive expressions for the nth-order interval distribution, its variance, and the serial correlation coefficients of the interspike intervals (ISIs) and confirm these analytical results by computer simulations. The theory is then applied to experimental data from electroreceptors of paddlefish, which have two distinct types of internal noisy oscillators, one forcing the other. The theory provides an analytical description of their afferent spiking statistics during spontaneous firing, and replicates a pronounced dependence of ISI serial correlation coefficients on the relative frequency of the driving oscillations, and furthermore allows extraction of certain parameters of the intrinsic oscillators embedded in these electroreceptors.
Highlights
Oscillatory activity is common in neural systems
When discussing our explicit results, we focus on changes of the interspike intervals (ISIs) statistics upon varying the ratio w of the frequency of stochastic oscillations to the neuron’s firing rate, a parameter that shows a remarkable effect for the electroreceptor afferents of paddlefish
We aim at (i) the statistics of individual interspike intervals (ISI) by means of their probability density function, its coefficient of variation (CV), and its skewness, and (ii) the correlations between ISIs as quantified by the serial correlation coefficient (SCC). We study these statistics for the perfect integrate-and-fire (PIF) model and compare the theoretical results to experimental data
Summary
Oscillatory activity is common in neural systems. Mechanical oscillations form an important class of sensory stimuli, for instance, in hearing, but may be generated autonomously by mechanosensory hair cells [1]. Stochastic oscillations are frequently found in neural systems, there is generally poor understanding of how an input current of this kind affects the firing pattern of a neuron, its ability to transmit information about time-dependent stimuli, and its interaction with other cells in a neural network. This is in marked contrast to the often studied (non-stationary) problem of how a deterministic periodic driving affects neural activity The simplest yet non-trivial problem that comes up with stochastic oscillations is how they shape the spontaneous activity of a spiking neuron, our topic here
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