Berlin 2024 – scientific programme
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BP: Fachverband Biologische Physik
BP 32: Tissue Mechanics II
BP 32.8: Talk
Thursday, March 21, 2024, 17:00–17:15, H 2032
Continuum mechanics of apical constriction — •Chandraniva Guha Ray1,2,3, Marija Krstic2,3, and Pierre Haas1,2,3 — 1Max Planck Institute for the Physics of Complex Systems — 2Max Planck Institute of Molecular Cell Biology and Genetics — 3Center for Systems Biology Dresden
Apical constriction, the contraction of apical cell sides, is a common mechanism driving deformations of biological tissues during development. It is associated with the geometric singularity in which cell cross-sections become triangular and hence the cell sides are maximally bent, splaying the cells and thus bending the cell sheet.
Here, we explore the mechanical consequences of this geometric singularity in what is perhaps the simplest problem of tissue buckling: Under external compression, a monolayer of cells buckles, and, as the compression is increased further, fans of triangular cells expand from the crests and troughs of the buckled shape. Taking a continuum limit of a "differential-tension model" describing the cell mechanics [1], we show how these expanding fans lead to a strong increase of the resistance of the tissue to further compression. We reveal an intriguing secondary bifurcation beyond the onset of triangular cells: The buckling amplitude of a thin monolayer increases with increasing compression until the cells touch sterically, but, surprisingly, the buckling amplitude of a thick monolayer decreases with increasing compression. We develop a scaling argument to describe this bifurcation, and discuss its consequences for tissue development.
[1] P. A. Haas and R. E. Goldstein, Phys. Rev. E 99, 022411 (2019)
Keywords: Buckling; Continuum mechanics; Apical constriction