Role of tensile stress in actin gels and a symmetry-breaking instability

It has been observed experimentally that the actin gel grown from spherical beads coated with polymerization enzymes spontaneously breaks the symmetry of its spherical shape, and yields a "comet" pushing the bead forward. We propose a mechano-chemical coupling mechanism for the initialization of this symmetry breaking. Key assumptions are that the dissociation of the gel takes place mostly in the region of the external surface, and that the rates of the dissociation depend on the tensile stress in the gel. We analyze a simplified two-dimensional model with a circular substrate. Our analysis shows that the symmetric steady state is always unstable against the inhomogeneous modulation of the thickness of the gel layer, for any radius of the circular substrate. We argue that this model represents the essential feature of three-dimensional systems for a certain range of characteristic lengths of the modulation. The characteristic time of the symmetry-breaking process in our model depends linearly on the radius of curvature of the substrate surface, which is consistent with experimental results, using spherical latex beads as substrate. Our analysis of the symmetry-breaking phenomenon demonstrates aspects of mechano-chemical couplings that should be working in vivo as well as in vitro.