Local interaction in retinal ganglion cell mosaics can generate a consistent spatial periodicity in cortical functional maps

Orientation map is one of the most studied functional maps in visual cortex, but the developmental mechanism of its consistent spatial periodicity is still elusive. Recently, a theoretical model suggested that a moiré interference pattern between ON and OFF retinal ganglion cell (RGC) mosaics can develop a quasi-periodic orientation map, but it is remained unclear how this can explain the constant periodicity of the maps [1]. Here we suggest a developmental model that a simple local interaction in RGCs can generate a consistent spatial periodicity of orientation preference, by inducing (i) a hexagonal lattice structure in ON/OFF RGC mosaics and (ii) a constant alignment angle between them.

First, we introduced a developmental model of a monotypic RGC mosaic to show that a local repulsive interaction can generate a hexagonal structure (Figure 1A). Previously, in the model study of the pairwise interaction point process, it was suggested that a local interaction alone cannot develop a long-range order in the mosaic structure [2]. We assumed a different type of local repulsive interaction that the cell positions can be gradually shifted by a repulsion from the neighbor cells and confirmed that this model can develop a long-range ordered structure that is well fitted to a hexagonal lattice.

Figure 1

Simulation of RGC mosaics and orientation map. A. Development of monotypic mosaic and auto-correlation. B. Heterotypic interaction depends on inter-layer distance. C. Moiré interference pattern of ON/OFF RGC mosaics. D. Simulated orentation map. E. Hexagonal pattern in auto-correlation of orientation map.

Next, we assumed that there also exists a heterotypic repulsive interaction between ON and OFF RGC mosaics and examined how this can affect the alignment between the two mosaics (Figure 1B). When the inter-layer distance between ON/OFF mosaics was varied within a proper interval, the hexagonal structure was preserved in each mosaic, but the alignment angle (θ) between the two mosaics was restricted within a certain range of angles, and this induced a constant spatial periodicity in the ON/OFF interference pattern (Figure 1C). As observed in the moiré interference, we confirmed a consistent hexagonal periodicity in the cortical orientation map that are simulated by statistical wiring model from the developed RGC mosaics (Figure 1D,E) [3].

Conclusions

Our result suggests that a local repulsive interaction in RGC mosaics can generate a hexagonal structure in ON/OFF RGC mosaics and a restricted alignment between them. The interference between mosaics induces a consistent spatial periodicity in cortical orientation map as predicted by the moiré interference pattern.