  Recent experiments in various cell types have shown that two-dimensional
tissues often display local nematic order, with evidence of extensile stresses
manifest in the dynamics of topological defects. Using a mesoscopic model where
tissue flow is generated by fluctuating traction forces coupled to the nematic
order parameter, we show that the resulting tissue dynamics can spontaneously
produce local nematic order and an extensile internal stress. A key element of
the model is the assumption that in the presence of local nematic alignment,
cells preferentially crawl along the nematic axis, resulting in anisotropy of
fluctuations. Our work shows that activity can drive either extensile or
contractile stresses in tissue, depending on the relative strength of the
contractility of the cortical cytoskeleton and tractions by cells on the
extracellular matrix.
