Physical Model of Cellular Symmetry Breaking

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.Symmetry breaking in physics is an old well-known concept. It is based on energy considerations: A symmetrical system can lose its symmetry if an asymmetrical state has a lower energy. The initial symmetrical state can be either unstable or metastable. In the latter case, there is an energy barrier to be overcome before symmetry breaking occurs. An external trigger can drive the system from its symmetrical to its asymmetrical state, but simple noise can also do so if its amplitude is sufficiently high. A simple example is a clown balancing on a ball: When the clown is standing on top of the ball, the system has a cylindrical symmetry (Fig. 1A). However, this state is unstable: The slightest perturbation will cause the clown to fall down in some direction, breaking the cylindrical symmetry (Fig. 1B). Imagine now that the ball is slightly flat on its base, giving more stability to the clown. Such a state is metastable: The clown can make small excursions safely (Fig. 1C,D), but if he moves too much (i.e., generates too much “noise”), he will fall down in this case also (Fig. 1E,F).Open in a separate windowFigure 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).Symmetry breaking is ubiquitous in physics, and can lead to phase transitions or pattern formation. It is also an important theme in cell biology, in which polarization is crucial for proper functioning of the cell. Cell polarization typically occurs in response to certain external or internal triggers. A well-known example is chemotaxis, in which a chemical gradient leads to polarization and directed movement of bacterium cells. Polarization also occurs during cytokinesis, in which intracellular stimuli triggered by the mitotic spindle determine the position of the cleavage furrow (Burgess and Chang 2005). Interestingly, cells conserve the ability to polarize even in the absence of an asymmetric signal (Devreotes and Zigmond 1988). For example, chemotactic cells that are presented a uniform concentration of chemoattractant polarize and move in random directions. Another example is blebbing, the spontaneous appearance of bare membrane bulges in some cells.Symmetry breaking in biological systems is a complex phenomenon, because biological systems are always out of equilibrium. Hence, symmetry breaking is not just a transition to a state of lower potential energy. Instead, active, dynamic processes must be considered that feed energy into the system. A biochemical explanation for symmetry breaking was given by Alan Turing. In a seminal paper in 1952 (Turing 1952), he showed that patterns can be generated by simple chemical reactions if the reactants have different diffusion rates. To make this clear, he considered the hypothetical situation in which the morphology of a cell (or cell clump) is determined by two chemical substances (called morphogens). These morphogens also control their own production rate: One enhances morphogen production (the activator) and the other inhibits morphogen production (the inhibitor). It was shown that a spatially homogeneous distribution of morphogens is unstable if the activator diffuses more slowly than the inhibitor. In this case, small stochastic concentration fluctuations are amplified, leading to a chemical instability (“a Turing instability”) and the formation of concentration gradients (or patterns). Reaction–diffusion models of the Turing type have been widely explored to explain polarization and biological development (Gierer and Meinhardt 1972; Sohrmann and Peter 2003; Wedlich-Soldner and Li 2003).Although reaction–diffusion models have proven to be very successful, there is increasing evidence that cell polarization is not only a matter of biochemistry; mechanical aspects play an important role too. Recent work suggests that spontaneous polarization can also be driven by a mechanical instability of the actomyosin cortex of cells. In the remainder of this review, we focus on such mechanical instabilities.