  The motility of a fish keratocyte on a flat substrate exhibits two distinct
regimes: the non-migrating and the migrating one. In both configurations the
shape is fixed in time and, when the cell is moving, the velocity is constant
in magnitude and direction. Transition from a stable configuration to the other
one can be produced by a mechanical or chemotactic perturbation. In order to
point out the mechanical nature of such a bistable behaviour, we focus on the
actin dynamics inside the cell using a minimal mathematical model. While the
protein diffusion, recruitment and segregation govern the polarization process,
we show that the free actin mass balance, driven by diffusion, and the
polymerized actin retrograde flow, regulated by the active stress, are
sufficient ingredients to account for the motile bistability. The length and
velocity of the cell are predicted on the basis of the parameters of the
substrate and of the cell itself. The key physical ingredient of the theory is
the exchange among actin phases at the edges of the cell, that plays a central
role both in kinematics and in dynamics.
