Physical model of cellular symmetry breaking

Abstract

Cells can polarize in response to external signals, such as chemical gradients, cell-cell contacts, and electromagnetic fields. However, cells can also polarize in the absence of an external cue. For example, a motile cell, which initially has a more or less round shape, can lose its symmetry spontaneously even in a homogeneous environment and start moving in random directions. One of the principal determinants of cell polarity is the cortical actin network that underlies the plasma membrane. Tension in this network generated by myosin motors can be relaxed by rupture of the shell, leading to polarization. In this article, we discuss how simplified model systems can help us to understand the physics that underlie the mechanics of symmetry breaking.

Figure 1.

Illustration of symmetry breaking with a clown standing on a balloon. In (A), the clown is in unstable equilibrium and the situation is symmetrical. However, any movement will make him fall down and the system (clown + balloon) then loses its symmetry. (B) If the balloon is slightly flat on its base (C–F), then the system is metastable, i.e., a slight perturbation of the clown will not break the symmetry (C, D), whereas a larger perturbation will destabilize the clown (F).

Figure 2.

Scheme for different cases of cortex relaxation in cellular events. (Blue rods) actin filaments, (red dumbbells) myosin fibers, (green patches) membrane attachments, (brown rods) microtubules, (brown dots) centrosomes. Curved arrows indicate the direction of cortex flows. (A) At the onset of cytokinesis, spindle microtubules have been proposed to cause cortex relaxation at the poles of the cell. The relaxed regions expand, leading to cleavage furrow formation. (B) In the Caenorhabditis elegans embryo, shortly after meiosis II, the sperm centrosome triggers cortex relaxation. The cortex then flows away from the relaxed region, leading to polarity protein segregation and pseudocleavage furrow formation. (C) Blebs form at sites of local detachment of the membrane from the cortex (top) or at sites of local cortex rupture (bottom). Cortex detachment from the membrane is sometimes followed by local cortex disassembly at the base of the bleb. Note that under certain conditions, multiple blebs can form. (© Paluch et al. 2006. Originally published in The Journal of Cell Biology. doi: 10.1083/jcb.200607159.)

Figure 3.

Analogy of the tension state in an actin gel growing from a bead surface and in the cell cortex. (A–C) Growing from a bead surface. (D–F) in the cell cortex. (A and D) Schematic view of the symmetry breaking of an actin gel growing from the surface of a bead (A) or the breakage of the cell cortex (D). (Blue rods) actin filaments, (red dumbbells) myosin fibers, (green patches) membrane attachments, (orange dots) actin polymerization activators. In both cases, a tension (T) builds up because of polymerization in curved geometry for the gel on the bead and because of the presence of myosin motors in the cortex. Rupture of the gel leads to actin shell or cortical movement (curved arrows). (B) Time lapse of a symmetry-breaking event (arrowhead) preceding the actin-based movement of a bead (epifluorescence microscopy with actin-AlexaFluor594). The first three images were taken 21, 24, and 40 minutes after the start of incubation, respectively. The last image shows the comet that develops eventually. (Images are reprinted from van der Gucht et al. 2005.) (C) Phase-contrast images of beads of different diameters (1 µm for the left image and 2.8 µm for the three other images) at low gelsolin concentration. (Images were provided by M. Courtois, Institut Curie, Paris, France.) (E) Time lapse of cortex breakage (arrowhead) and bleb growth in an L929 fibroblast fragment expressing actin-GFP. Fluorescence images are projections from a three-dimension reconstruction (time between images is 20 seconds). (Images are reprinted from Paluch et al. 2005.) (F) Time lapse of a cell displaying multiple blebs. Confocal images of an L929 fibroblast expressing actin-GFP were taken at 0, 25, and 35 seconds. (Images were provided by J.-Y. Tinevez and E. Paluch, Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany.) Bars (B and C), 10 µm; (E and F), 5 µm. (© Paluch et al. 2006. Originally published in The Journal of Cell Biology. doi: 10.1083/jcb.200607159.)