A migrating epithelial monolayer flows like a Maxwell viscoelastic liquid

We perform a bidimensional Stokes experiment in an active cellular material: an autonomously migrating monolayer of Madin-Darby Canine Kidney (MDCK) epithelial cells flows around a circular obstacle within a long and narrow channel, involving an interplay between cell shape changes and neighbour rearrangements. Based on image analysis of tissue flow and coarse-grained cell anisotropy, we determine the tissue strain rate, cell deformation and rearrangement rate fields, which are spatially heterogeneous. We find that the cell deformation and rearrangement rate fields correlate strongly, which is compatible with a Maxwell viscoelastic liquid behaviour (and not with a Kelvin-Voigt viscoelastic solid behaviour). The value of the associated relaxation time is measured as $\tau = 70 \pm 15$~min, is observed to be independent of obstacle size and division rate, and is increased by inhibiting myosin activity. In this experiment, the monolayer behaves as a flowing material with a Weissenberg number close to one which shows that both elastic and viscous effects can have comparable contributions in the process of collective cell migration.