  Recent experiments suggest that the interplay between cells and the mechanics
of their substrate gives rise to a diversity of morphological and migrational
behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a
visco-elastic substrate. We compare our model with experiments on endothelial
cells plated on polyacrylamide hydrogels to constrain model parameters and test
predictions. Our analysis reveals that morphology and migratory behavior are
determined by an intricate interplay between cellular polarization and
substrate strain gradients generated by traction forces exerted by cells
(self-haptotaxis).
