Dynamical Pattern Selection of Growing Cellular Mosaic in Fish Retina

TL;DR

This paper introduces a Markovian lattice model to explain how specific retinal mosaic patterns in fish are naturally selected during growth, highlighting the role of local defects in pattern formation.

Contribution

The study presents a novel model and analysis that elucidate the mechanism behind dynamical pattern selection in growing fish retina mosaics.

Findings

Radial stripe pattern is naturally selected during retina growth.

Local defects are crucial for the emergence of the wild-type pattern.

Numerical simulations and theoretical analyses support the pattern selection mechanism.

Abstract

A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during the retina growth, against the geometrically equivalent, circular stripe pattern. The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, which find that the successive emergence of local defects plays a critical role in the realization of the wild-type pattern.