Cell migration is a fundamentally important phenomenon underlying wound healing, tissue development, immune response and cancer metastasis. Understanding basic physics of the cell migration presented a great challenge until, in the last three decades, a combination of biological, biophysical and mathematical approaches shed light on basic mechanisms of the cell migration. I will describe two models, based on nonlinear partial differential equations and free boundary problems, which predicted that individual cells do not linger in a symmetric stationary state for too long, but rather spontaneously break symmetry and initiate motility. The cells can either crawl straight, or turn, depending on mechanical parameters. I will show how experimental data supported the models, and I will also review current computational challenges.

Alex' URL: https://cims.nyu.edu/~mogilner/