Hydrodynamic instabilities, waves and turbulence in spreading epithelia

TL;DR

This paper develops a hydrodynamic model of epithelial monolayers as active viscous fluids, explaining observed wave phenomena and turbulence, and providing new insights into collective cell behavior and force transmission.

Contribution

It introduces a novel hydrodynamic framework that captures epithelial dynamics, including nonlinear waves and turbulence, challenging elasticity-based interpretations.

Findings

Viscous fluid model explains slow epithelial dynamics.

Prediction of nonlinear wave regimes and turbulence.

Flow-polarity coupling explains plithotaxis.

Abstract

We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. We show that a viscous fluid model explains a variety of observations on the slow dynamics of epithelial monolayers, in particular those that had been interpreted before as signatures of elasticity. The non-elastic nature of the waves can be tested on the basis of simple predictions of the model. Our theoretical framework provides new insights such as the interpretation of plithotaxis as a result of a strong flow-polarity coupling, and the quantification of collective force-transmission of cells in terms of the non-locality of interactions. In addition, we study the nonlinear regime of those waves deriving an exact map of the model into the Complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the very unstable and irregular dynamics often observed in epithelia.