(A) model study on the developmental mechanism of consistent spatial periodicity in orientation map in visual cortex

Abstract

The orientation map is of great interest among functional maps in the visual cortex, but its developmental mechanism has been quite controversial among researchers. Recently, a theoretical model suggested that a moire interference pattern between ON and OFF retinal ganglion cell (RGC) mosaics can develop a quasi-periodic orientation map (Paik and Ringach, 2011), but the question remains how this interference pattern can generate a consistent spatial periodicity. Here, we suggest a developmental model in which a local interaction between cells can develop a long-range ordered hexagonal lattice mosaics, and a heterotypic interaction can control the alignment between ON/OFF mosaics. This provides an answer to above question about the development of a consistent periodicity in orientation maps. First, how a local repulsive interaction can generate a long-range ordered structure in RGC mosaics was examined. Previously, it was reported that the pairwise interaction point process (PIPP) model, in which cell positions are determined by a birth-and-death procedure that only considers a local interaction between homotypic pairs (Eglen et al., 2005) could not develop a long-range ordered structure in the mosaic (Hore et al., 2012). Here, rather than a birth-and-death step, it was assumed that cell positions can be gradually shifted by a local re-pulsive interaction between nearby cells. Thus, computer simulations were performed on the development of monotypic model RGC mosaics. It was confirmed that this local interaction model can develop a hexagonal pattern and also a long-range order periodicity in a monotypic mosaic. Next, it was assumed that there exists not only a homotypic interaction but also a het-erotypic repulsive interaction between ON/OFF mosaics

and thus, how this can affect the alignment between two mosaics was examined. By simultaneously simulating the develop-ment of both mosaics, the heterotypic interaction significantly alters the alignment between two mosaics. In addition, when the distance between two mosaics (inter-mosaic distance) was varied, it was observed that the alignment angle between two mosaics was restricted within a certain range of the inter-mosaic distance, which is required by the moir？ interference model for orientation map development. Additionally, the existence of a heterotypic correlation was also estimated in simulat-ed and observed mosaics. After development, if one mosaic is intentionally shifted slightly, the repulsive energy state will be destabilized. If the energy state is estimated for various shifts of one mosaic, it will show a band of higher energy state compared to the mosaics with-out any shifts and such band was observed in both the observed and simulated mosaics. This suggests that local interaction between heterotypic cells might have been applied during the development of observed RGC mosaics, which is opposite of the previous assumption in an-other model (Eglen et al., 2005). This dissertation suggests that a simple local interaction between RGCs can develop a long-ranged structure in the mosaic, and that when ON and OFF mosaics are developed with a heterotypic repulsive interaction within a certain range of distance between the layers, the alignment angle between the ON and OFF mosaics can be restricted, and this leads to a con-sistent spatial periodicity of the orientation map. To support above results, the existence of a correlation between heterotypic pairs in the observed mosaic was also estimated. Therefore, this model provides a complementary explanation of how an interference pattern in the retinal mosaic structure can be developed as a blueprint of cortical orientation maps.