[POS] Biomathematics

[POS-60] Tiling mechanisms of the Drosophila compound eye:A potential role of the cellular force

*Ting ZHENG¹ (1. Kanazawa University (Japan))

Keywords:

Drosophila Compound eye,cell morphogenesis,anisotropic force,cellular force,vertex model

Tile patterns refer to the orderly arrangement of many cells and are found in a variety of multicellular organisms. The Drosophila compound eye is a fascinating example of such tiling, showing a regular arrangement of repeating units called ommatidia. Hexagonal patterns, common in wild-type eyes, provide mechanical robustness, while tetragonal patterns have also been observed in certain mutants with reduced eye size. Laser ablation experiments in the previous study by Hayashi et al. revealed increased tissue-wide tension along the dorsoventral axis in these tetragonal mutants. However, the vertex model, a common mathematical model used to calculate cell shape according to mechanical stability, does not reproduce the hexagonal to tetragonal transition. Building on the findings of Hayashi et al., the Voronoi diagram effectively recapitulates this hexagonal to tetragonal transition in response to the dorsoventral stretching of the eye tissue, suggesting that the cellular concentric expansion force, which is absent in the vertex model, may play an important role in tile pattern formation. However, the nature of this cellular expansion force remains unknown. The radial actin fibers found in the ommatidial cells may provide such an anisotropic force. By incorporating dorsoventral stretching and anisotropic force into the vertex model, we successfully reproduced the transition from hexagonal to tetragonal patterns. This finding underscores the essential role of anisotropic cellular force in tile pattern formation and suggests a refined vertex model framework that can explore broader phenomena in cellular morphogenesis and mechanical adaptation.