  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 that is characteristic of
epithelial tissues 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 epithelial unjamming 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. As
such, curvature-induced unjamming emerges as a novel mechanism for epithelial
layer fluidization. Our quantitative model proposes the existence of a new,
extended, phase diagram wherein local cell shape, cell propulsion, and tissue
geometry combine to determine the epithelial migratory phenotype.
