Effective Viscosity in a Collectively Migrating Epithelial Cell Monolayer

Within an epithelial tissue, cells slide past their neighbors to produce shape changes required for processes ranging from tissue development to cancer metastasis. Although the cell forces and motion are both experimentally measurable, it is not yet possible to relate the two, because the sources of energy injection and dissipation within an epithelial cell layer are not clear. Here, we investigate how energy is injected and dissipated by studying the relationship between shear stresses and strain rates within an epithelial cell monolayer. Confluent monolayers of MDCK epithelial cells were imaged over time using optical microscopy. The stress tensor within the plane of the cell layer was quantified with monolayer stress microscopy, and the strain rate tensor was quantified from the velocity field, which was measured by digital image correlation. Both stresses and strain rates varied substantially over space and time. Comparison of shear stress against shear strain rate within windows at different locations in space revealed linear correlations, with the slope being an effective viscosity. Perturbations that increased and decreased the amount of fibrous actin within the cells respectively increased and decreased the average effective viscosity. Surprisingly, there emerged multicellular regions in which the effective viscosity was negative. Regions of negative effective viscosity consistently exhibited greater cell speed and vorticity, and the cells had elevated metabolic activity, which reflects an increased energy demand in these cells. These results indicate that effective viscosity is a useful means of quantifying the flow of energy in living matter.