Physics-Biology interface seminar: Doron Grossman


11:00 - 12:00

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Instabilities and Geometry of Growing Tissues

Doron Grossman (College de France – for this work; LadHyX, Ecole polytechnique – current)

We present a covariant continuum formulation of a generalized two-dimensional vertexlike model
of epithelial tissues which describes tissues with different underlying geometries, and allows for an
analytical macroscopic description. Using a geometrical approach and out-of-equilibrium
statistical mechanics, we calculate both mechanical and dynamical instabilities of a tissue, and
their dependences on various variables, including activity, and cell-shape heterogeneity (disorder).
We show how both plastic cellular rearrangements and the tissue elastic response depend on the
existence of mechanical residual stresses at the cellular level. Even freely growing tissues may
exhibit a growth instability depending on the intrinsic proliferation rate. Our main result is an
explicit calculation of the cell pressure in a homeostatic state of a confined growing tissue. We
show that the homeostatic pressure can be negative and depends on the existence of mechanical
residual stresses. This geometric model allows us to sort out elastic and plastic effects in a growing,
flowing, tissue.

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