  Motility initiation in crawling cells requires transformation of a symmetric
state into a polarized state. In contrast, motility arrest is associated with
re-symmetrization of the internal configuration of a cell. Experiments on
keratocytes suggest that polarization is triggered by the increased
contractility of motor proteins but the conditions of re-symmetrization remain
unknown. In this paper we show that if adhesion with the extra-cellular
substrate is sufficiently low, the progressive intensification of motor-induced
contraction may be responsible for both transitions: from static (symmetric) to
motile (polarized) at a lower contractility threshold and from motile
(polarized) back to static (symmetric) at a higher contractility threshold. Our
model of lamellipodial cell motility is based on a 1D projection of the complex
intra-cellular dynamics on the direction of locomotion. In the interest of
analytical transparency we also neglect active protrusion and view adhesion as
passive. Despite the unavoidable oversimplifications associated with these
assumptions, the model reproduces quantitatively the motility initiation
pattern in fish keratocytes and reveals a crucial role played in cell motility
by the nonlocal feedback between the mechanics and the transport of active
agents. A prediction of the model that a crawling cell can stop and
re-symmetrize when contractility increases sufficiently far beyond the motility
initiation threshold still awaits experimental verification.
