Collective Motility, Mechanical Waves, and Durotaxis in Cell Clusters

When epithelial cell clusters move in a collective manner on a substrate mechanical signals play a major role in organizing the coherent behavior. There are a number of unexplained experimental results from traction force microscopy for a system of this type (MDCK cell clusters). These include: the internal strains are tensile even for clusters that expand by proliferation; the tractions on the substrate are confined to the edges of the cluster; in many cases there are density waves within the cluster; there is collective durotaxis of the cluster even though individual cells show no effect; and for cells in an annulus there is a transition between expanding clusters with proliferation and non-proliferating cases where cells rotate around the annulus. We formulate a simplified mechanical model which explains all of these effects in a straight-forward manner. The central feature of the model is to use a molecular clutch picture which allows "stalling" -- inhibition of cell contraction and motility by external forces. Stalled cells are passive elements from a physical point of view and the un-stalled cells are active. When we attach cells to the substrate and to each other, and take into account contact inhibition of locomotion, we get a simple picture that gives all the mechanical results noted above. Supplementary information can be downloaded at: https://drive.google.com/file/d/1leyvqk0OuDhkyCw8iaIMk1uKNwgs1ey0/view?usp=sharing