Early stages of collective cell invasion: Biomechanics

The early stages of the collective invasion may occur by single mesenchymal cells or hybrid epithelial-mesenchymal cell groups that detach from cancerous tissue. Tumors may also emit invading protrusions of epithelial cells, which could be led (or not) by a basal cell. Here we devise a novel fractional step cellular Potts model comprising passive and active cells able to describe these different types of collective invasion before cells start proliferating. Cells moving toward stiffness gradients (durotaxis) and active forces pulling them away from the tumor have different symmetry properties under cellular extension and retraction that sometimes hamper collective invasion when put together. Thus, these forces are included in different half steps of the fractional step method. Compared with a single step method, fractional step produces more realistic collective invasion scenarios with little extra computational effort. Biochemical mechanisms that determine how cells acquire their different phenotypes and cellular proliferation will be incorporated to the model in future publications.