Characteristic Effects of Stochastic Oscillatory Forcing on Neural Firing: Analytical Theory and Comparison to Paddlefish Electroreceptor Data

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.Author Summary: We explore how a neuron responds to a special type of input signal which is oscillatory but noisy (narrow-band noise). These fluctuations could be due to sensory input, due to oscillatory activity of a surrounding network, or due to a natural stimulus. We study theoretically the effects of noisy oscillations on an idealized model neuron, which would otherwise produce as output a series of action potentials at regular intervals. Because our model is comparably simple, we can describe the effects on ISI statistics analytically with formulas that we test against computer simulations of the model. Moreover, we can compare our theoretical predictions to experimental data from electroreceptors of paddlefish - a biological example for spiking neurons that are naturally stimulated by stochastic oscillatory input. In particular, our theory provides a simple explanation of the seemingly complicated patterns of correlations between interspike intervals, that are observed for the electro-afferents in paddlefish; the theory shows also good agreement with respect to other independent spike train statistics. Our findings further the understanding of how nervous activity is shaped by oscillatory noisy signals, which can emerge in the neural networks of the brain, in the sensory periphery, and in the environment.