Speaker: Ido Lavi, University of Barcelona
Title: Motility and morphodynamics of confined cells
Under physiological conditions, immune cells and cancer cells typically move through highly restricted 3D environments. Several studies have shown that physical confinement can trigger fast amoeboid modes of motility quite distinct from the well-known crawling of keratocytes on flat substrates. Many squeezed cell patterns remain poorly understood, indicating the need for appropriate mathematical descriptions. In this context, we shall discuss a minimal model of migration and deformation of a cell confined between two parallel surfaces. This description likens the cytosol to a viscous droplet driven out of equilibrium by an actomyosin boundary force. The classic Hele-Shaw problem is then coupled to the internal advection-diffusion transport of a force-transducing solute. While fairly simple and tractable, this model supports a variety of cell-like behaviors, including spontaneous-symmetry-breaking (polarization), traveling-wave solutions (migrating steady states), and shape-concentration oscillations. The predicted moving shapes, in particular, share distinct similarities with various observations. To explore regimes of strong deformation and include external impediments such as walls and constrictions, we developed a finite-element moving-mesh simulation that efficiently computes stable numerical approximations of the free-boundary dynamics. Using this tool, one may also handle many related sharp-interface problems in 2D.