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arXiv · 2504.16765

Geometry of T1 transitions in epithelia

Pierre A. Haas
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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.

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Pierre A. Haas. 2025-04-23. Geometry of T1 transitions in epithelia. https://doi.org/10.1103/kdnb-bxdx

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