A unified neural network [corrected] model of spatiotemporal processing in X and Y retinal ganglion cells. I. Analytical results.

This work presents unified analyses of spatial and temporal visual information processing in a feed-forward network of neurons that obey membrane, or shunting equations. The feed-forward shunting network possesses properties that make it well suited for processing of static, spatial information. However, it is shown here that those same properties of the shunting network that lead to good spatial processing imply poor temporal processing characteristics. This article presents an extension of the feed-forward shunting network model that solves this problem by means of preprocessing layers. The anatomical interpretation of the resulting model is structurally analogous to recently discovered data on a retinal circuit connecting cones to retinal ganglion cells through pairs of push-pull bipolar cells. Mathematical analysis of the lumped model leads to the hypothesis that X and Y retinal ganglion cells may consist of a single mechanism acting in different parameter ranges. This hypothesis is confirmed in the companion article, wherein the model--in conjunction with a nonlinear temporal adaptation mechanism--is used to reproduce experimental data of both X and Y cells by simple changes in morphological and physiological parameters.