Inference of mechanical stresses within the actively migrating cell sheet

Collective cell migration is important in numerous physiological phenomena such as airway remodeling, cancer invasion and metastasis, and development. When epithelial cells migrate collectively they typically do so as a confluent monolayer, which is a form of active matter. As the monolayer migrates actively across a planar substrate, it develops internal stresses within the layer, some part of which are transmitted to that substrate and thus provide propulsive forces. These propulsive forces at the cell-substrate interface are called tractions. Our lab has shown that if the traction distribution is measured, then one can recover the internal 2D in-plane stresses within a monolayer; this method is called Monolayer Stress Microscopy(MSM). The MSM approach assumes that the monolayer behaves as an elastic sheet, and stresses are calculated numerically with a finite elements scheme. To alleviate the need for a numerical scheme, and thereby simplify stress recovery, here we revisit the problem using a hydrodynamical formulation. We derive a novel 3D analytical solution that recovers internal stresses and velocities from tractions directly, and requires no numerics. We are currently comparing the analytical solution and experiments.