Viscoelastic properties of epithelial cells subject to shape changes were monitored by indentation-retraction/relaxation experiments. MDCK II cells cultured on extensible polydimethylsiloxane substrates were laterally stretched and, in response, displayed increased cortex contractility and loss of excess surface area. Thereby, the cells preserve their fluidity but inevitably become stiffer. We found similar behavior in demixed cell monolayers of ZO-1/2 double knock down (dKD) cells, cells exposed to different temperatures and after removal of cholesterol from the plasma membrane. Conversely, the mechanical response of single cells adhered onto differently sized patches displays no visible rheological change. Sacrificing excess surface area allows the cells to respond to mechanical challenges without losing their ability to flow. They gain a new degree of freedom that permits resolving the interdependence of fluidity β on stiffness $${K}_{{{{{{{{\rm{A}}}}}}}}}^{0}$$ K A 0 . We also propose a model that permits to tell apart contributions from excess membrane area and excess cell surface area.
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