On the relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer

Cells migrate collectively in physiological phenomena including cancer metastasis, development, and asthmatic airway remodeling. Within an epithelial monolayer, for example, each constituent cell exerts intercellular stresses on neighboring cells, and exerts traction forces on its substrate. While traction forces exerted by a monolayer have been measured for more than a decade, their relationship to measured cellular velocities remains unknown. Additionally, the relationship between intercellular stresses and tractions also remains unresolved. In passive systems, traction stresses and velocities are linked in principle through a constitutive law. The simplest and commonly assumed form of such a law is a Newtonian fluid, which implies a linear relationship between stress and strain rate. In this talk, I will address the question: To what extent are tractions related to velocities through such a linear constitutive law? Using a newly derived theoretical model, I will show that the tractions predicted from the measured velocity field are uncorrelated with the measured tractions. This implies that current methods for intercellular stress recovery need to be corrected where one such rectification is the inclusion of an active stress term, for which we derive a novel constraint.