The different behaviors of colonies of two cell lines, ARO (thyroid carcinoma-derived cells) and MLP-29 (mouse liver progenitor cells), in response to hepatocyte growth factor (HGF) are described deducing suitable cellular Potts models (CPM). It is shown how increased motility and decreased adhesiveness are responsible for cell-cell dissociation and tissue invasion in the ARO cells. On the other hand, it is shown that, in addition to the biological mechanisms above, it is necessary to include directional persistence in cell motility and HGF diffusion to describe the scattering and the branching processes characteristic of MLP-29 cells.