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

Abstract

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.

Cytoskeletal Symmetry Breaking and Chirality: From Reconstituted Systems to Animal Development

“…Above a critical force value that depends on the actin coats thickness, the network will break at an imperfection. To robustly observe symmetry breaking in these systems, coat polymerization and/or de-polymerization has to be controlled in a way that the coat does not become too thick [103,104], thereby reaching a metastable state where small fluctuations in tensile stress can yield coat rupture.…”

A Physical Model of Cellular Symmetry Breaking

“…Such a nucleation mechanism process is also characterized by a much larger variation in symmetry breaking rates among different beads (van der Gucht et al 2005). As discussed in Sekimoto et al 2004, symmetry breaking could be enhanced in this case if the depolymerization rate is also affected by the stresses in the gel.…”

“…Polymerization occurs at the surface of the bead (where filaments are nucleated), whereas depolymerization occurs at the pointed ends that are assumed to be mostly situated near the exterior of the gel (Noireaux et al 2000;Sekimoto et al 2004). Thus, the growth velocity of the gel can be described as follows:…”

Nanoscale dynamics and aging of fibrous peptide-based gels

“…[6][7][8][9][10][11][12][13][14] To do so, extant theories (and many simulations as well) have appealed to approximations that are not generally justified by the underlying chemical kinetics. For example, it is commonly assumed that nonequilibrium considerations are important only for the discrete, driven part of the ratcheting process; all other degrees of freedom are imagined to follow adiabatically.…”

“…This assumption of rapid equilibration is explicit in some stochastic models of polymerization ratchets, [6][7][8][9][10] implicit in some phenomenological models of actin gels, 11,12 and inherent to continuum models of growing gels. 13,14 While this effective-force approximation can be justified on thermoa) Electronic mail: evanhohlfeld@gmail.com b) Electronic mail: geissler@berkeley.edu dynamic grounds when external loads are sufficiently strong to stall the ratchet, 8 most biological ratchets operate far from stall conditions.…”