  Collective cell motions underlie structure formation during embryonic
development. Tissues exhibit emergent multicellular characteristics such as
jamming, rigidity transitions, and glassy dynamics, but there remain questions
about how those tissue scale dynamics derive from local cell level properties.
Specifically, there has been little consideration of the interplay between
local tissue geometry and cellular properties influencing larger scale tissue
behaviours. Here we consider a simple two dimensional computational vertex
model for confluent tissue monolayers, which exhibits a rigidity phase
transition controlled by the shape index (ratio of perimeter to square root
area) of cells, on a spherical surface. We show that the critical point for the
rigidity transition is a function of curvature such that more highly curved
systems are more likely to be in a less rigid, more fluid, phase. A phase
diagram we generate for the curvature and shape index constitutes a testable
prediction from the model. The curvature dependence is interesting because it
suggests a natural explanation for more dynamic tissue remodelling and facile
growth in regions of higher surface curvature, without invoking the need for
biochemical or other physical differences. This has potential ramifications for
our understanding of morphogenesis of budding and branching structures.
