Aydar Uatay

• Cell migration is essential for embryogenesis, wound healing, immune surveillance, and progression of diseases, such as cancer metastasis. For the migration to occur, cellular structures such as actomyosin cables and cell-substrate adhesion clusters must interact. As cell trajectories exhibit a random character, so must such interactions. Furthermore, migration often occurs in a crowded environment, where the collision outcome is deter- mined by altered regulation of the aforementioned structures. In this work, guided by a few fundamental attributes of cell motility, we construct a minimal stochastic cell migration model from ground-up. The resulting model couples a deterministic actomyosin contrac- tility mechanism with stochastic cell-substrate adhesion kinetics, and yields a well-defined piecewise deterministic process. The signaling pathways regulating the contractility and adhesion are considered as well. The model is extended to include cell collectives. Numer- ical simulations of single cell migration reproduce several experimentally observed results, including anomalous diffusion, tactic migration, and contact guidance. The simulations of colliding cells explain the observed outcomes in terms of contact induced modification of contractility and adhesion dynamics. These explained outcomes include modulation of collision response and group behavior in the presence of an external signal, as well as invasive and dispersive migration. Moreover, from the single cell model we deduce a pop- ulation scale formulation for the migration of non-interacting cells. In this formulation, the relationships concerning actomyosin contractility and adhesion clusters are maintained. Thus, we construct a multiscale description of cell migration, whereby single, collective, and population scale formulations are deduced from the relationships on the subcellular level in a mathematically consistent way.