  We investigate numerically the dynamics of shape and displacement
fluctuations of two-dimensional flexible vesicles filled with active particles.
At low concentration most of the active particles accumulate at the boundary of
the vesicle where positive particle number fluctuations are amplified by
trapping, leading to the formation of pinched spots of high density, curvature
and pressure. At high concentration the active particles cover the vesicle
boundary almost uniformly, resulting in fairly homogeneous pressure and
curvature, and nearly circular vesicle shape. The change between polarized and
spherical shapes is driven by the number of active particles. The
center-of-mass of the vesicle performs a persistent random walk with a long
time diffusivity that is strongly enhanced for elongated active particles due
to orientational correlations in their direction of propulsive motion.
  In our model shape-shifting induces directional sensing and the cell
spontaneously migrate along the polarization direction.
