Rigidity transitions in confluent and mesenchymal biological tissues

In animal morphogenesis and the design of shape-changing materials, one successful strategy is to poise the system near a fluid-solid or floppy-rigid transition. Near such transitions, small changes to material parameters can drive enormous changes in mechanical response. As in glass-blown ornaments, targeted fluidization facilitates large deformations, while targeted solidification drives the system to inherent states that remain largely immobile, both of which are useful for function. In confluent biological tissues, where there are no gaps between cells, there is strong evidence that tissues leverage ‘second-order rigidity’ to control the transition. I will discuss a new theoretical framework that describes the critical manifold of all possible second-order rigid states in vertex models for confluent tissues, which allows us to understand the properties of states poised near a fluid-transition and investigate design or evolution strategies near the manifold. In stellate mesenchymal tissues, where there are large gaps between cells, recent experiments suggest a different strategy for morphogenetic control – the tissue is fluid-like with regular cellular rearrangements that allow large-scale deformation, but it nevertheless maintains a system-spanning tensioned network like a solid. I will discuss our recent work to develop a model that explains this emergent behavior and identifies key cell-scale features required to create it.