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Description
In vertebrate retinas, multiple types of cone photoreceptors, each sensitive to different wavelengths, exhibit various two-dimensional arrangements. In zebrafish, each of four cone types (blue, red, green, and UV) appears periodically, forming a nearly square lattice, called “cone mosaic”. Such regularity seems to realize uniform color resolution across the retina.
Regular mosaic patterns are considered to emerge from irregular arrangements through cell rearrangements. A previous mathematical model postulated that cells move on a two-dimensional lattice (\cite{tohya}). In this model, cell movement was affected by cell adhesion between contacting cells, whose strength depended on the combination of contacting cell types. In addition, a red-green cone pair was assumed to contact strongly to form a “double cone”. Contact of other cells with the double cone was restricted orthogonally: either the red or the green cone only (single-side) or both at once (double-side). Thus, the red-green pair aligned along one of the four directions (←,↓,↑,→).
We introduced four additional oblique directions in the double cone orientations. Our model allows larger freedom in the dynamics, revealing that optimal parameters of the adhesion strength for mosaic formation only partially overlap with the previous ones. Moreover, mosaics can be formed even when single-side adhesion of the double cone is weaker than double-side adhesion, unlike the previous result favoring stronger single-side adhesion.
Bibliography
@article{tohya,
title = {Difference in the {Retinal} {Cone} {Mosaic} {Pattern} {Between} {Zebrafish} and {Medaka}: {Cell}-{Rearrangement} {Model}},
volume = {221},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {00225193},
shorttitle = {Difference in the {Retinal} {Cone} {Mosaic} {Pattern} {Between} {Zebrafish} and {Medaka}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0022519303931924},
doi = {10.1006/jtbi.2003.3192},
language = {en},
number = {2},
urldate = {2026-03-10},
journal = {Journal of Theoretical Biology},
author = {Tohya, Shusaku and Mochizuki, Atsushi and Iwasa, Yoh},
month = mar,
year = {2003},
pages = {289--300},
}
