Cells on spheres: glassy dynamics of vertex models in curved space

The analogy between cellular monolayers and aggregates on the one hand and jammed solids or colloidal glasses on the other has provided a powerful framework for probing questions of rigidity, motilitiy, and collective excitations in dense biological tissues. However, simple coarse-grained theoretical models of these systems — such as vertex or Voronoi models of confluent cells — have both an unusual zero-temperature rigidity transition and highly anomalous glassy dynamics. The underlying reasons for these atypical behaviors are poorly understood. Here we begin to discriminate between theoretical explanations by numerically studying cellular models embedded on the surface of a sphere. By introducing constant Gaussian curvature we lift the large degenerate space of zero-energy modes that contributes to the unusual jamming transition of vertex-like models, and explore how this changes the finite-temperature glassy dynamics.