Symmetry Breaking

A. van Oudenaarden & J.A. Theriot, Nature Cell Biology 1, 493 (1999)

• "Cooperative symmetry-breaking by actin filament polymerization in a model for cell motility"
  • Figure 1. Symmetry-breaking in a cloud of actin filaments

• Some form of positive feedback is necessary for symmetry breaking
  • Figure 2. The multifilament stochastic model

Allen Lee, Ha Youn Lee, and M. Kardar, Phys. Rev. Lett. 95, 138101 (2005)

1. What is a simple, generic model for the stationary/moving transition?
2. How does the shape of the bead influence this transition?
3. How are the fluctuations of an active bead different from those of a Brownian bead?

(a) Polymerizing actin exerts force on bead   [g(Ω,t): effective force/actin density]

(b) Net force pushes bead

(c) Actin dynamics influenced by local velocity of bead surface

Eliminating fast modes leads to an effective (stochastic) equation for the velocity:

"Phase diagram and critical behavior" (noiseless):

• Numerical confirmation of scaling of symmetry breaking time

Nonspherical Beads:

• Instability is typically along the direction offering the largest cross-sectional view,

• M. F. Carlier et al, BioEssays 25, 336 (2003)

• Singularities are determined by bead symmetries:

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