Epithelial layer fluidization by curvature-induced unjamming.

The transition of an epithelial layer from a stationary, quiescent state to a highly migratory, dynamic state is required for wound healing, development, and regeneration. This transition, known as the unjamming transition (UJT), is responsible for epithelial fluidization and collective migration. Previous theoretical models have primarily focused on the UJT in flat epithelial layers, neglecting the effects of strong surface curvature characteristic of the epithelium \textit{in vivo}. In this study, we investigate the role of surface curvature on tissue plasticity and cellular migration using a vertex model embedded on a spherical surface. Our findings reveal that increasing curvature promotes the UJT by reducing the energy barriers to cellular rearrangements. Higher curvature favors cell intercalation, mobility, and self-diffusivity, resulting in epithelial structures that are malleable and migratory when small, but become more rigid and stationary as they grow. Together, these results provide a conceptual framework to better understand how cell shape, cell propulsion, and tissue geometry contribute to tissue malleability, remodeling, and stabilization.