# Anisotropic Cellular Forces Drive Hexagonal‐to‐Tetragonal Tiling Transitions in the Drosophila Eye

## TL;DR

This paper shows how anisotropic cellular forces influence the tiling patterns in the Drosophila eye, explaining transitions from hexagonal to tetragonal arrangements.

## Contribution

The study introduces an extended vertex model incorporating anisotropic forces to explain epithelial tiling transitions.

## Key findings

- Anisotropic forces from radial actin fibers drive tiling geometry changes in Drosophila eye mutants.
- The extended vertex model successfully reproduces hexagonal-to-tetragonal transitions.
- Disrupting radial actin fibers leads to irregular tiling, confirming the model's predictions.

## Abstract

Tile patterns are fundamental organizational principles of multicellular epithelial tissues. The Drosophila compound eye provides a striking example, in which ommatidia are arranged in a highly regular hexagonal lattice, while tetragonal patterns emerge in specific small‐eye mutants. Although increased dorsoventral tension has been implicated in this hexagonal‐to‐tetragonal transition, conventional vertex models fail to reproduce the observed pattern transformation, indicating the presence of additional uncharacterized force‐generating mechanisms. Here, we demonstrate that anisotropic cellular forces driven by radial actin fibers are a key determinant of ommatidial tiling geometry. By extending the vertex model to incorporate both dorsoventral stretching and anisotropic forces that generate rotational torque at cell boundaries, we successfully recapitulate the hexagonal‐to‐tetragonal transition observed in mutant eyes. Experimental disruption of radial actin fibers suppressed tetragonal pattern formation and induced irregular tiling, providing in vivo support for the model predictions. Importantly, in silico analyses further revealed that anisotropic forces play a dual role: while they drive tetragonalization under symmetry‐breaking conditions in mutant eyes, they stabilize regular hexagonal tiling in the wild‐type context. These findings identify anisotropic cellular forces as an essential component of epithelial pattern formation and establish an extended vertex model framework for understanding force‐driven morphogenetic transitions during development.