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

Abstract

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.

On the Origin of the Functional Architecture of the Cortex

“…Quasi-regularity implies that if we know that a cell is located in one specific location P , then the density of cells of the same class as a function of the distance from P is initially low at small distances, increases to peak above the mean density, and then settles down to the mean density at large distances (Fig 1b). The functional independence of the arrays means that knowing the location of one ON cell only tells us that an OFF cell cannot lie at the same location (Fig 1c) [51]. The simulated retinal ganglion cell mosaic in Fig 1a shows how these two features generate pairs of ON/OFF cells in close proximity.…”

“…To simulate the layout of X-RGC mosaics in the retina we have adopted the pair-wise interaction point process model (PIPP) [51]. Briefly, the method starts by randomly positioning n ON and n OFF cells on a simulated patch of retina of size L × L .…”

“…Third, the statistics of monosynaptic connectivity between the thalamus and layer 4 in the adult cortex are, so far, available only in the cat [45], [46]. Finally, the spatial statistics of the retinal ganglion cell mosaics in cat have been carefully measured and rigorously modeled [47]–[51].…”

Neuronal clustering and fasciculation phenotype in Dscam‐ and Bax‐deficient mouse retinas

“…L functions were tested for deviations from randomness by computing a U score for each L function and its 99 random simulations following previous approaches (Eglen et al, , 2005. The U score for an L function is the integrated distance between the L function and the mean of the other 99 L functions.…”

“…Note, though, that the other fields shown in figure 3b-d (for Dscam+/-, Bax-/-and Dscam-/-, respectively), are all significantly different from random distributions using such Monte Carlo testing ( figure 3j-l). Indeed, the insets above these L functions rank-order the U score of each of these 100 L functions (Eglen et al, 2003b;2005), this score being the difference of each L function from the mean of the other 99 L functions (shown as the central grey line within each envelope), as described by Diggle (1979). For this U score statistic, the lower the rank, the better the real data are fit by the random simulations.…”