Prize Talk: Lars Onsager PrizeSymmetries, broken symmetries and tissue dynamics*

Using generalized hydrodynamic theory, I will describe how a nematic epithelium can be totally at rest on a narrow stripe and spontaneously adopt a shearing motion on broader stripes. Such shearing motions are observed in cancer invasion. I will then describe experiments in which the substrate plays the role of an external orientational field on the nematic direction of the tissue. The simple case of a homogeneous field is for some cell lines spectacular: a new symmetry breaking toward a polar moving state is observed. Again generalized hydrodynamics allows to understand this polar symmetry breaking. I will then show that substrate curvature may play the role of external field and illustrate this statement with experiments investigating epithelium motion in hollow cylinders or on cylindrical fibers. Spontaneous symmetry breaking is again observed, with a continuous rotation of the tissue orthogonally to the cylinder axis. I will eventually argue that the physical approach to tissue dynamics is relevant to real life situations.