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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.

the journal of neuroscience/the journal of neuroscience

Competition between Retinal Ganglion Axons for Targets under the Servomechanism Model Explains Abnormal Retinocollicular Projection of Eph Receptor-Overexpressing or Ephrin-Lacking Mice