  Eukaryotic cells possess motility mechanisms allowing them not only to
self-propel but also to exert forces on obstacles (to push) and to carry
cargoes (to pull). To study the inherent asymmetry between active pushing and
pulling we model a crawling acto-myosin cell extract as a 1D layer of active
gel subjected to external forces. We show that pushing is controlled by
protrusion and that the macroscopic signature of the protrusion dominated
motility mechanism is concavity of the force velocity relation. Instead,
pulling is driven by protrusion only at small values of the pulling force and
it is replaced by contraction when the pulling force is sufficiently large.
This leads to more complex convex-concave structure of the force velocity
relation, in particular, competition between protrusion and contraction can
produce negative mobility in a biologically relevant range. The model
illustrates active readjustment of the force generating machinery in response
to changes in the dipole structure of external forces. The possibility of
switching between complementary active mechanisms implies that if necessary
'pushers' can replace 'pullers' and visa versa.
