Effect Of Cellular Rearrangement Time Delays On The Rheology Of Vertex Models For Confluent Tissues

Large-scale tissue deformation during biological processes such as morphogenesis requires cellular rearrangements. The simplest rearrangement in confluent cellular monolayers involves neighbor exchanges among four cells, called a T1 transition, in analogy to foams. But unlike foams, cells must execute a sequence of molecular processes, such as endocytosis of adhesion molecules, to complete a T1 transition. Such processes could take a long time compared to other timescales in the tissue. 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 time affect tissue mechanics, by quantifying the relaxation time of tissues in the presence of T1 delays and comparing that to the cell-shape based timescale that characterizes fluidity in the absence of any T1 delays. We show that the molecular-scale T1 delay timescale dominates over the cell shape-scale collective response timescale when the T1 delay time is the larger of the two. We extend this analysis to tissues that become anisotropic under convergent extension, finding similar results. Moreover, we find that increasing the T1 delay time increases the percentage of higher-fold coordinated vertices and rosettes, and decreases the overall number of successful T1s, contributing to a more elastic-like-and less fluid-like-tissue response. Our work suggests that molecular mechanisms that act as a brake on T1 transitions could stiffen global tissue mechanics and enhance rosette formation during morphogenesis.Author summary In various morphogenetic events such as embryonic development, tissue repair, or the spread of cancer tumors, cells must move past each other and change neighbors to allow global tissue shape change. In its simplest form, such cell rearrangement events involves neighbor exchanges among four cells, called T1 transitions. During a T1 transition, a sequence of molecular processes must occur over a finite time while cell junctions shrink and new junctions form. In this work, we augment vertex models to require a fixed, finite time for cellular rearrangements, which we call the "T1 delay time". We show that T1 delay affects tissue mechanics, stiffening the tissue. We also find that increasing the T1 delay time enhances the percentage of higher-fold coordinated vertices and rosettes, which are seen during many developmental processes such as during the body axis elongation of the fruit fly. Our results highlight the important role of a molecular-scale timescale, T1 delay time, on the global tissue response, and suggest that the organisms might utilize specific molecular processes that act as a brake on cellular rearrangements in order to control the global tissue response.