Eukaryotic cell motility requires coordination across three spatial size scales: intracellular signaling that regulates cell shape and movement, single cells motility (e.g. cells responding to extracellular signals), and collective cell behavior from a few cells to tissues (e.g. cells working together). Mathematical and computational models can assist in interpreting experiments and developing an understanding of cell behavior at many levels of organization. In this talk, I will focus on three collective phenomena: (1) repolarization; (2) cell entrainment and (3) cell cluster migration. At each of these spatial scales a different modelling approach is most suitable.
At the intra-cellular scale, I will use systems of reaction diffusion equations and bifurcation analysis to elucidate repolarization of small GTPases, which are central regulators of cell morphology and motility. Agent-based models inspired by colloidal physics are employed at the cellular scale to understand cell entrainment, and finally I will use non-local partial differential equations to elucidate cell cluster stability at the “tissue level”. At the tissue level, I will demonstrate how Morse potentials (a commonly used cell-cell interaction potential) can be derived, and how analysis of non-local PDEs can inform agent-based models.