  Blebs are cell protrusions generated by local membrane-cortex detachments
followed by expansion of the plasma membrane. Blebs are formed by some
migrating cells, for example primordial germ cells of the zebrafish. While
blebs occur randomly at each part of the membrane in unpolarized cells, a
polarization process guarantees the occurrence of blebs at a preferential site
and thereby facilitates migration towards a specified direction. Little is
known about the factors involved in development and maintenance of a polarized
state, yet recent studies revealed the influence of an intracellular flow and
the stabilizing role of the membrane-cortex linker molecule Ezrin. Based on
this information, we develop and analyse a coupled bulk-surface model
describing a potential cellular mechanism by which a bleb could be induced at a
controlled site. The model rests upon intracellular Darcy flow and a
diffusion-advection-reaction system, describing the temporal evolution from an
unpolarized to a stable polarized Ezrin distribution. We prove the
well-posedness of the mathematical model and show that simulations
qualitatively correspond to experimental observations, suggesting that indeed
the interaction of an intracellular flow with membrane proteins can be the
cause of the cell polarization.
