A model for the variability of maintained discharges and responses to flashes of light

Previous studies of the variability of firing of retinal ganglion cells have led to apparently contradictory conclusions. To a first approximation, maintained discharges derive their variability from a noise source that is linearly added to the signal setting the mean firing rate. On the other hand, the variability of responses to abrupt changes in lighting seems to result from a nonlinear interaction between signal and noise. In both the cat and the goldfish retinae, the variance of rate is a fractional power function of the mean response amplitude (impulses/s). The exponent of that power function depends on the duration of the period in which the response is sampled after each transition in luminance; longer durations have a larger exponent. These results are difficult to explain with any simple model. The variability of the maintained discharges also deviates from the predictions of simple additivity. We propose a model for the variability of responses to abrupt changes in lighting that incorporates variability of the form observed for maintained discharges. The parameters of our model that provide the best fits to the variability of responses also provide a reasonable fit to the variability of maintained discharges. Thus, a single explanation can account for the variability of maintained discharges and responses of ganglion cells.