An analysis of spatial summation in the receptive fields of goldfish retinal ganglion cells

Abstract

We have derived an analytical method for determining the processing hierarchy of a system in which more than one input influences the output; we have applied the technique to the summation of spatially separated areas within either the centers or surrounds of the receptive fields of goldfish retinal ganglion cells. Our method consists of obtaining intensity-response data for each of the two inputs alone and for both inputs applied simultaneously. From these data we construct two graphs: the response-summation plot is a plot of the physiological sum vs the algebraic sum: the sensitivity-summation plot is a plot of the summed individual sensitivities vs the sensitivity when both areas are stimulated. The responsesummation plot reveals non-linearities at or after the first interaction of the two areas: the sensitivity-summation plot reveals non-linearities at or before the final summation of the two areas. Using this method, we find that the processing in either the center or surround of a receptive field of a ganglion cell in the goldfish may be described by a square root function at the receptors, linear summation of the influences from the separate areas (with a threshold on each), and a compressive function following the summation. It is not necessary to postulate additional lateral interactions among sub-areas either in the center or in the surround.