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We show that actin lamellar fragments extracted from cells, lacking
the complex machinery for cell crawling, are spontaneously motile due
solely to actin polymerization forces at the boundary. The motility
mechanism is associated to a morphological instability similar to the
problem of viscous fingering in Hele-Shaw cells, and does not require
the existence of a global polarization of the actin gel, nor the
presence of molecular motors, contrary to previous claims. We base our
study on the formulation of a 2d free-boundary problem and exploit
conformal mapping and center manifold projection techniques to prove
the nonlinear instability of the center of mass, and to find an exact
and simple relation between shape and velocity. A complex subcritical
bifurcation scenario into traveling solutions is unfolded. With the
help of high-precision numerical computation we show that the velocity
is exponentially small close to the bifurcation points, implying a
non-adiabatic mechanism. Examples of traveling solutions and their
stability are studied numerically. Extensions of the approach to more
realistic descriptions of actual biological systems are briefly
discussed.
REF: C. Blanch-Mercader and J. Casademunt, Physical Review Letters
110, 078102 (2013)