The application of the Gierer-Meinhardt equations to the development of the retinotectal projection

Model calculations are presented for the several properties of the development of the retinotectal projection in amphibians and fishes, using the Gierer-Meinhardt equations. One of these properties is the maintenance of topographic mapping between the retina and the tectum during their development despite the fact that the two tissues grow in morphologically different ways. Another is the existence of a "critical period", at which the coordinates of the retina with respect to the tectum are irrevocably determined. It is assumed that the connections between the retinal and the tectal cells are made on the correspondence of positional markers which are given as a form of the distribution of a specific activator, the dynamics of which is described by the Gierer-Meinhardt equations. The monotonic distributions of the activator and the existence of the critical period are shown by a computer simulation of the proliferating retina. Several changes of the retinotectal projection after surgical operations on the retina or the tectum are also explained.