  A motile cell, when stimulated, shows a dramatic increase in the activity of
its membrane, manifested by the appearance of dynamic membrane structures such
as lamellipodia, filopodia and membrane ruffles. The external stimulus turns on
membrane bound activators, like Cdc42 and PIP2, which cause increased branching
and polymerization of the actin cytoskeleton in their vicinity leading to a
local protrusive force on the membrane. The emergence of the complex membrane
structures is a result of the coupling between the dynamics of the membrane,
the activators and the protrusive forces. We present a simple model that treats
the dynamics of a membrane under the action of actin polymerization forces that
depend on the local density of freely diffusing activators on the membrane. We
show that, depending on the spontaneous membrane curvature associated with the
activators, the resulting membrane motion can be wave-like, corresponding to
membrane ruffling and actin-waves, or unstable, indicating the tendency of
filopodia to form. Our model also quantitatively explains a variety of related
experimental observations and makes several testable predictions.
