Role of cellular rearrangement time delays on the rheology of vertex models for confluent tissues

Morphogenesis involve global-scale changes to the tissue, and in confluent tissues, large-scale deformation requires cell rearrangements. In its simplest form, a cell rearrangement involves neighbor exchanges among four cells, called a T1 transition. In order to complete the T1, a sequence of molecular processes, such as endocytosis of adhesion molecules, must occur over a finite time. In this work, we incorporate this idea by augmenting vertex models to require a fixed, finite time for T1 transitions, which we call the “T1 delay time”. We study how variations in T1 delay affect tissue mechanics, by quantifying the relaxation time of tissues in the presence of T1 delays and comparing to the cell-shape based timescale that characterizes fluidity in the absence of any T1 delays. We show the molecular-scale T1 delay timescale dominates over the cell shape-scale collective response timescale when the T1 delay is the larger of the two. We extend this analysis to anisotropic tissues under convergent extension, finding similar results. We also find correlations between the rate of extension and rosette formation. The T1 delay time could be a mechanism to regulate tissue mechanics and rosette formation during morphogenesis.