  During the spreading of epithelial tissues, the advancing tissue front often
develops fingerlike protrusions. Their resemblance to traditional viscous
fingering patterns in driven fluids suggests that epithelial fingers could
arise from an interfacial instability. However, the existence and physical
mechanism of such a putative instability remain unclear. Here, based on an
active polar fluid model for epithelial spreading, we analytically predict a
generic instability of the tissue front. On the one hand, active cellular
traction forces impose a velocity gradient that leads to an accelerated front,
which is, thus, unstable to long-wavelength perturbations. On the other hand,
contractile intercellular stresses typically dominate over surface tension in
stabilizing short-wavelength perturbations. Finally, the finite range of
hydrodynamic interactions in the tissue selects a wavelength for the fingering
pattern, which is, thus, given by the smallest between the tissue size and the
hydrodynamic screening length. Overall, we show that spreading epithelia
experience an active fingering instability based on a simple kinematic
mechanism. Moreover, our results underscore the crucial role of long-range
hydrodynamic interactions in the dynamics of tissue morphology.
