Motility and morphodynamics of confined cells

We present a minimal hydrodynamic model of polarization, migration, and deformation of a biological cell confined between two parallel surfaces. In our model [1], the cell cytoplasm is likened to a viscous droplet that is driven out of equilibrium by an active cytsokeleton force. This force acts on the cell membrane and is modulated locally by an internal diffusive solute. While fairly simple and analytically tractable, this two-dimensional sharp-interface model predicts a range of compelling cell-like behaviors. A linear stability analysis reveals that solute activity first destabilizes a global polarization-translation mode, prompting motility through spontaneous symmetry breaking. At higher activity, the system crosses a series of Hopf bifurcations leading to coupled oscillations of droplet shape and solute concentration profiles. At the nonlinear level, we find traveling-wave solutions associated with unique polarized shapes that resemble experimental observations. Altogether, this model offers an analytical paradigm of active deformable systems in which viscous hydrodynamics are coupled to diffusive force transducers.