Statistical properties of spike trains: Universal and stimulus-dependent aspects

Statistical properties of spike trains measured from a sensory neuron in vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike trains exhibit universal behavior over a short time, modulated by a stimulus-dependent envelope over a long time. A model of the neuron as a nonlinear oscillator driven by noise and by an external stimulus is suggested to account for these results. In the short-time universal regime, the main biophysical effect is refractoriness, which can be described as a repulsive ( 1/x) interaction law among spikes. A universal distribution function for intervals is found, defining a point process with special symmetry properties. The long-time modulations in the spike train are related in a simple way to the properties of the input stimulus as seen through the neuronal nonlinearity. Thus our model enables a separation of the effects of internal neuronal properties from the effect of external stimulus properties. Explicit formulas are derived for different statistical properties, which are in very good agreement with the data in both the universal and the stimulus-dependent regimes.