Rigidity of 3D confluent tissue is governed by energy barriers to local reconnection events

Cellular-based models of tissue can undergo rigidity transitions. We investigate three-dimensional vertex model for confluent

tissue, where the bulk tissue is represented by a tessellation of polyhedral cells with shared faces, using Brownian dynamics. In this model,

a rigidity transition appears to occur as a function of the target shape index of the cells at low effective temperatures. In the rigid phase,

the system is frustrated and the average shape parameter does not reach the target value. In the fluid phase, the average shape parameters

for the cells track the target value. Here, motivated from similar studies in two dimensions, we develop numerical methods to study the

energy cost of driving individual reconnection events within the bulk three dimensional tissue model. These reconnection events are a

three-dimensional analog of the two-dimensional T1 transitions studied in foams, colloids, and vertex models. We find that the energy cost

is a function of the target shape index, pointing to a potential mechanism driving the transition to fluidity. We further study these forced

reconnection events in a model of tissue embedded in extra cellular matrix to quantify how an external coupling of bulk tissue to collagen

can influence the onset of fluidity in the tissue.