Emergence of radial orientation selectivity: Effect of cell density changes and eccentricity in a layered network

We establish a simple mechanism by which radially oriented simple cells can emerge in the primary visual cortex. In 1986, R. Linsker. proposed a means by which radially symmetric, spatial opponent cells can evolve, driven entirely by noise, from structure in the initial synaptic connectivity distribution. We provide an analytical derivation of Linsker's results, and further show that radial eigenfunctions can be expressed as a weighted sum of degenerate Cartesian eigenfunctions, and vice-versa. These results are extended to allow for radially dependent cell density, from which we show that, despite a circularly symmetric synaptic connectivity distribution, radially biased orientation selectivity emerges in the third layer when cell density in the first layer, or equivalently, synaptic radius, changes with eccentricity; i.e., distance to the center of the lamina. This provides a potential mechanism for the emergence of radial orientation in the primary visual cortex before eye opening and the onset of structured visual input after birth.