Competition between retinal ganglion axons for targets under the servomechanism model explains abnormal retinocollicular projection of Eph receptor-overexpressing or ephrin-lacking mice.

Topographic mapping of retinal ganglion axons to the midbrain is computed by the servomechanism model, which is based on the experimental result of cell attachment. Cells expressing a certain level of Eph proteins (receptors for ephrin ligands) optimally attach to a surface that expresses a specific level of ephrin ligand density. The retina has an increasing nasal-to-temporal gradient of Eph receptor density, and the optic tectum/superior colliculus has an increasing rostral-to-caudal gradient of membrane-bound ephrin ligand. An axon from the retina has an identification tag of a certain level of Eph receptor density depending on its retinal position and adheres to the site on the tectum/superior colliculus expressing ephrin ligands at a critical ligand density level. Quantitatively, a retinal axon has a receptor density (R) that is determined by its retinal position, and the axon terminal is induced to adhere to the tectal site of ligand density (L = S/R), where S is a constant. Consequently, the servomechanism model defines positions of axon terminals on the midbrain. Abnormal topographic maps are reported in a knock-in experiment with elevated density of Eph receptors and a knock-out experiment lacking ephrin ligands using gene-targeting technology. By adding competition between axon terminals for target sites to the servomechanism model, the abnormal maps became easy to understand. Furthermore, the servomechanism-competition model allowed conjecture of the gradient shapes of receptor and ligand densities and estimation of the capacity of the midbrain surface to accept retinal axon terminals.