Geometry of T1 transitions in epithelia
arXiv:2504.16765 · doi:10.1103/kdnb-bxdx
Abstract
The flows of tissues of epithelial cells often involve T1 transitions. These neighbour exchanges are irreversible rearrangements crossing an energy barrier. Here, by an exact geometric construction, I determine this energy barrier for general, isolated T1 transitions dominated by line tensions. I~show how deviations from regular cell packing reduce this energy barrier, but find that line tension fluctuations increase it on average. By another exact construction, I prove that the nonlinear tensions in vertex models of tissues also resist T1 transitions. My results thus form the basis for coarse-grained understanding of cell neighbour exchanges for continuum descriptions of epithelia.
8 pages, 3 figures; Supplemental Material: 4 pages, 4 figures
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