# Active Fingering Instability in Tissue Spreading

## TL;DR

This paper demonstrates that epithelial tissue spreading can exhibit an active fingering instability driven by cellular forces and hydrodynamic interactions, leading to fingerlike protrusions during tissue expansion.

## Contribution

It introduces an active polar fluid model predicting a generic instability in tissue front dynamics, highlighting the role of hydrodynamics and cellular forces in tissue morphology.

## Key findings

- Active cellular traction induces a velocity gradient causing instability.
- Contractile stresses stabilize short wavelengths.
- Hydrodynamic interactions determine fingering pattern wavelength.

## Abstract

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.