Homotypic constraints dominate positioning of on- and off-center beta retinal ganglion cells

Beta retinal ganglion cells (RGCs) of the cat are classified as either on-center or off-center, according to their response to light. The cell bodies of these on- and off-center RGCs are spatially distributed into regular patterns, known as retinal mosaics. In this paper, we investigate the nature of spatial dependencies between the positioning of on- and off-center RGCs by analysing maps of RGCs and simulating these patterns. We introduce principled approaches to parameter estimation, along with likelihood-based techniques to evaluate different hypotheses. Spatial constraints between cells within-type and between-type are assumed to be controlled by two univariate interaction functions and one bivariate interaction function. By making different assumptions on the shape of the bivariate interaction function, we can compare the hypothesis of statistical independence against the alternative hypothesis of functional independence, where interactions between type are limited to preventing somal overlap. Our findings suggest that the mosaics of on- and off-center beta RGCs are likely to be generated assuming functional independence between the two types. By contrast, allowing a more general form of bivariate interaction function did not improve the likelihood of generating the observed maps. On- and off-center beta RGCs are therefore likely to be positioned subject only to homotypic constraints and the physical constraint that no two somas of opposite type can occupy the same position.