Mathematical model of retinal mosaic formation

Mathematical Modeling of Retinal Mosaic Formation by Mechanical Interactions and Dendritic Overlap

The retina is a complex assembly of neurons packed into a three-layer structure containing five classes of cells. Each class of retinal cells is regularly arranged within its layer in an orderly configuration called the retinal mosaic. We have set up a mathematical model of retinal mosaic formation focusing on the actions of local mechanical forces on the neuron's cytoskeleton. The cytoskeleton has been modeled according to two approaches, one based on the tensegrity concept (a structure made of elastic and rigid elements), and the other based on a simple model with viscoelastic features. We have assumed causing deformation of their cytoskeleton, overlap of dendritic areas and movement of the neuron. Simulations based on these two models indicate that a random distribution of neurons reaches an orderly configuration by local and mechanical neuron interaction in the case in which the cytoskeleton is modeled using the tensegrity approach, but not when the neuron is modeled as a purely viscoelastic system. Considering that the main structural difference between the Maxwell model and the tensegrity model is that the latter model contains rigid elements whereas the former does not, this suggests that the presence of rigid components in the cytoskeleton of retinal neurons plays a key role in the formation processes of the retinal mosaic.