[MS11] Dynamics of Pattern Formation and Morphogenesis in Biological Systems

[MS11-01] Geometric Constraints and Their Role in Epithelial Folding Patterns

*Yasuhiro Inoue¹, Kaito Kuninishi¹, Tomohiro Mimura¹ (1. Kyoto University (Japan))

Keywords:

Folding patterns,Geometric constraints,Cell division,Cell center model,Morphogenesis

During morphogenesis, epithelial tissues develop characteristic folding patterns that are essential for proper organ formation. This study investigates how geometric constraints influence folding pattern formation in spherical shell epithelial tissues. Using multi-cellular mechanical simulations with a cell center model applied to epithelial cells arranged on a spherical shell, we examined how tissue growth through cell division generates distinct folding patterns under various geometric conditions. Our results demonstrate that two key geometric parameters significantly determine the resulting folding morphology: the radius of the spherical shell and the strength of radial deformation constraints. As the radius increases, folding patterns transition from hexagonal-like structures to maze-like patterns. Similarly, variations in radial constraint strength affect the fineness and complexity of the emerging patterns. Further analysis revealed that the dimensionless parameter R/L (radius to equilibrium cell distance ratio) serves as a critical determinant of pattern type. When comparing simulations with equivalent R/L values but different absolute dimensions, similar folding patterns emerge, suggesting that this ratio fundamentally governs pattern formation. These findings provide insights into how geometric constraints drive morphological diversity in epithelial tissues and highlight the importance of physical parameters in developmental processes.