  Epithelial cell clusters often move collectively on a substrate. Mechanical
signals play a major role in organizing this behavior. There are a number of
experimental observations in these systems which await a comprehensive
explanation. These include: the internal strains are tensile even for clusters
that expand by proliferation; the tractions on the substrate are often confined
to the edges of the cluster; there can exist density waves within the cluster;
clusters can exhibit collective durotaxis when individual cells show no effect;
and for cells in an annulus there is a transition between expanding clusters
with proliferation and the case where cells fill the annulus and rotate around
it. We formulate a mechanical model to examine these effects. We use a
molecular clutch picture which allows "stalling" -- inhibition of cell
contraction by external forces. Stalled cells are passive from a physical point
of view and the un-stalled cells are active. By attaching cells to the
substrate and to each other, and taking into account contact inhibition of
locomotion, we get a simple picture for many of these findings as well as
predictions that could be tested.
  SI text/figures included, SI movies at
https://rice.box.com/s/xiy3mwsfj3203lfu7pk0udfklexcgsew
