Spontaneous motility of actin-based cell fragments as a free-boundary problem

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)