  The motility of a cell can be triggered or inhibited not only by an applied
force but also by a mechanically neutral force couple. This type of loading,
represented by an applied stress and commonly interpreted as either squeezing
or stretching, can originate from extrinsic interaction of a cell with its
neighbors. To quantify the effect of applied stresses on cell motility we use
an analytically transparent one-dimensional model accounting for active myosin
contraction and induced actin turnover. We show that stretching can polarize
static cells and initiate cell motility while squeezing can symmetrize and
arrest moving cells. We show further that sufficiently strong squeezing can
lead to the loss of cell integrity. The overall behavior of the system depends
on the two dimensionless parameters characterizing internal driving (chemical
activity) and external loading (applied stress). We construct a phase diagram
in this parameter space distinguishing between, static, motile and collapsed
states. The obtained results are relevant for the mechanical understanding of
contact inhibition and the epithelial-to-mesenchymal transition.
