Modeling the variability of firing rate of retinal ganglion cells

Impulse trains simulating the maintained discharges of retinal ganglion cells were generated by digital realizations of the integrate-and-fire model. If the mean rate were set by a "bias" level added to "noise," the variability of firing would be related to the mean firing rate as an inverse square root law; the maintained discharges of retinal ganglion cells deviate systematically from such a relationship. A more realistic relationship can be obtained if the integrate-and-fire mechanism is "leaky"; with this refinement, the integrate-and-fire model captures the essential features of the data. However, the model shows that the distribution of intervals is insensitive to that of the underlying variability. The leakage time constant, threshold, and distribution of the noise are confounded, rendering the model unspecifiable. Another aspect of variability is presented by the variance of responses to repeated discrete stimuli. The variance of response rate increases with the mean response amplitude; the nature of that relationship depends on the duration of the periods in which the response is sampled. These results have defied explanation. But if it is assumed that variability depends on mean rate in the way observed for maintained discharges, the variability of responses to abrupt changes in lighting can be predicted from the observed mean responses. The parameters that provide the best fits for the variability of responses also provide a reasonable fit to the variability of maintained discharges.