Energy injection in an epithelial cell monolayer indicated by negative viscosity

Epithelial tissues are driven out of thermodynamic equilibrium by internally generated forces, causing complex patterns of motion. Even when both the forces and motion are measurable, it is not yet possible to relate the two, because the sources of energy injection and dissipation are often unclear. Here, we study how energy is transferred by developing a method to measure the effective viscosity from the shear stresses and strain rates within an epithelial cell monolayer. Interestingly, there emerged multicellular regions in which the relationship between shear stress and shear strain rate was negatively proportional, indicating a negative effective viscosity. The negative effective viscosity occurred in regions wherein cell stresses were less efficient at producing tissue deformations compared to regions of positive effective viscosity. Regions of negative effective viscosity consistently exhibited greater cell speed and vorticity, and the cells had elevated metabolic activity, reflecting an increased energy demand in these cells. Our study shows that negative effective viscosity is a useful means of quantifying the flow of energy in living matter.