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We study the vertex model for epithelial tissue mechanics extended to includecoupling between the cell shapes and tensions in cell-cell junctions. Thiscoupling represents an active force which drives the system out of equilibriumand leads to the formation of nematic order interspersed with prominent,long-lived $+1$ defects. The defects in the nematic ordering are coupled to theshape of the cell tiling, affecting cell areas and coordinations. Thisintricate interplay between cell shape, size, and coordination provides apossible mechanism by which tissues could spontaneously develop long-rangepolarity through local mechanical forces without resorting to long-rangechemical patterning.

Shape-tension coupling produces nematic order in an epithelium vertex model