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

The relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer are currently unknown. Ten years ago, a method known as Monolayer Stress Microscopy (MSM) was suggested from which the intercellular stresses could be computed given a traction field. The core assumption of MSM is that the intercellular stresses within the monolayer obey a linear and passive constitutive law such as a Hookean solid or a Newtonian fluid. Due to the lack of independently measured intercellular stresses, a direct validation of the 2D stresses predicted by MSM is presently not possible. An alternative approach, which we give here and denote as the Stokes method, is based on simultaneous measurements of the monolayer velocity field and the cell/substrate tractions. Using the same assumptions as those underlying MSM, the velocity field suffices to compute tractions, from which we can then compare with those measured by traction force microscopy. We find that the calculated tractions and measured tractions are uncorrelated. From which it follows that some serious modification of the underling rheology is needed. We will discuss a number of alternatives including the contribution of active stresses for which we have derived a novel constraint.