  Based on symmetry consideration of migration and shape deformations, we
formulate phenomenologically the dynamics of cell crawling in two dimensions.
Forces are introduced to change the cell shape. The shape deformations induce
migration of the cell on a substrate. For time-independent forces we show that
not only a stationary motion but also a limit cycle oscillation of the
migration velocity and the shape occurs as a result of nonlinear coupling
between different deformation modes. Time-dependent forces are generated in a
stochastic manner by utilizing the so-called coherence resonance of an
excitable system. The present coarse-grained model has a flexibility that it
can be applied, e.g., both to keratocyte cells and to Dictyostelium cells,
which exhibit quite different dynamics from each other. The key factors for the
motile behavior inherent in each cell type are identified in our model.
