  Observations of single epidermal cells on flat adhesive substrates have
revealed two distinct morphological and functional states, namely a
non-migrating symmetric unpolarized state and a migrating asymmetric polarized
state. These states are characterized by different spatial distributions and
dynamics of important biochemical cell components: F-actin and myosin-II form
the contractile part of the cytoskeleton, and integrin receptors in the plasma
membrane connect F-actin filaments to the substratum. In this way, focal
adhesion complexes are assembled, which determine cytoskeletal force
transduction and subsequent cell locomotion. So far, physical models have
reduced this phenomenon either to gradients in regulatory control molecules or
to different mechanics of the actin filament system in different regions of the
cell.
  Here we offer an alternative and self-organizational model incorporating
polymerization, pushing and sliding of filaments, as well as formation of
adhesion sites and their force dependent kinetics. All these phenomena can be
combined into a non-linearly coupled system of hyperbolic, parabolic and
elliptic differential equations. Aim of this article is to show how relatively
simple relations for the small-scale mechanics and kinetics of participating
molecules may reproduce the emergent behavior of polarization and migration on
the large-scale cell level.
