Symmetry Breaking in Biology

Symmetry breaking is essential for cell movement, polarity, and developmental patterning. Amplification of initial asymmetry is key to the conserved mechanisms involved.Tyger! Tyger! burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?
– William Blake     

Magnetic-Based Double Fano Resonances in Au-SiO2-Si Multilayer Nanoshells

Plasmonics - Compared to metallic nanostructures employed in plasmonics, dielectric materials with high refractive index can directly engineer magnetic responses in addition to the electric...     

Mechanochemical Symmetry Breaking in Hydra Aggregates

Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra.     

Chiral Symmetry Breaking in Large Peptide Systems

Chiral symmetry breaking in far from equilibrium systems with large number of amino acids and peptides, like a prebiotic Earth, was considered. It was shown that if organic catalysts were abundant, then effective averaging of enantioselectivity would prohibit any symmetry breaking in such systems. It was further argued that non-linear (catalytic) reactions must be very scarce (called the abundance parameter) and catalysts should work on small groups of similar reactions (called the similarity parameter) in order to chiral symmetry breaking have a chance to occur. Models with 20 amino acids and peptide lengths up to three were considered. It was shown that there are preferred ranges of abundance and similarity parameters where the symmetry breaking can occur in the models with catalytic synthesis / catalytic destruction / both catalytic synthesis and catalytic destruction. It was further shown that models with catalytic synthesis and catalytic destruction statistically result in a substantially higher percentage of the models where the symmetry breaking can occur in comparison to the models with just catalytic synthesis or catalytic destruction. It was also shown that when chiral symmetry breaking occurs, then concentrations of some amino acids, which collectively have some mutually beneficial properties, go up, whereas the concentrations of the ones, which don’t have such properties, go down. An open source code of the whole system was provided to ensure that the results can be checked, repeated, and extended further if needed.

     

Highly-Tunable Magnetic and Electric Responses in the Perforated Au-SiO2-Si Multilayer Nanoshells

Plasmonics - In this work, we have demonstrated that the perforated Au-SiO2-Si multilayer nanoshells can support additional magnetic response besides electric response, where Si core provides...     

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.     

Lipid Aggregates Inducing Symmetry Breaking in Prebiotic Polymerisations

It is a long-standing and still open problem to determine the origin of biomolecular homochirality, and many scenarios have been suggested. Amphiphilic molecules are renowned for their capability to reorganize themselves in a variety of different morphologies and topologies, and for their capability to partition chemicals in well defined domains. Here a possible role for amphiphilic molecules inducing symmetry breaking is suggested in the framework of the research on origin of life.     

Cellular Symmetry Breaking during Caenorhabditis elegans Development

The nematode worm Caenorhabditis elegans has produced a wellspring of insights into mechanisms that govern cellular symmetry breaking during animal development. Here we focus on two highly conserved systems that underlie many of the key symmetry-breaking events that occur during embryonic and larval development in the worm. One involves the interplay between Par proteins, Rho GTPases, and the actomyosin cytoskeleton and mediates asymmetric cell divisions that establish the germline. The other uses elements of the Wnt signaling pathway and a highly reiterative mechanism that distinguishes anterior from posterior daughter cell fates. Much of what we know about these systems comes from intensive study of a few key events—Par/Rho/actomyosin-mediated polarization of the zygote in response to a sperm-derived cue and the Wnt-mediated induction of endoderm at the four-cell stage. However, a growing body of work is revealing how C. elegans exploits elements/variants of these systems to accomplish a diversity of symmetry-breaking tasks throughout embryonic and larval development.Over the past few decades, the C. elegans embryo has become a premiere system for studying cellular symmetry breaking in a developmental context. During C. elegans development, nearly every division produces daughter cells with different developmental trajectories. In some cases, these differences are imposed on daughters before or after division through inductive signals, but many of these divisions are intrinsically asymmetric—an initial symmetry-breaking step creates polarized distributions or activities of factors that control developmental potential. Registration of the cleavage plane with the axis of polarity then ensures differential inheritance of these potentials. With respect to cell fates, the output of these asymmetric divisions is amazingly diverse, yet the embryo seems to accomplish this diversity through variants of a few conserved symmetry-breaking systems. Thus the C. elegans embryo provides an exceptional opportunity to explore not only the core mechanisms underlying cellular symmetry breaking, but also how evolution can reconfigure these mechanisms to do different but related jobs in multiple contexts.In this review, we focus most of our attention on two conserved systems that together account for much of the cellular asymmetry observed during C. elegans embryogenesis. The first, which is best known for its role in the early asymmetric cell divisions that segregate germline from the soma, involves a complex interplay between Par proteins, Rho-family GTPases, and the actomyosin cytoskeleton. Interestingly, the embryo exploits elements of this same system to break symmetry during cleavage furrow specification and to establish apicobasal polarity in early embryonic cells and in the first true embryonic epithelia. The second system we focus on involves an unusual application of WNT signaling pathway components and is used reiteratively throughout embryonic and larval development to distinguish anterior and posterior daughter cell fates. Rather than comprehensively review these systems, we highlight topics not extensively covered in other reviews.     

Effect of Symmetry Breaking on Plasmonic Coupling in Nanoring Dimers

Plasmonics - Breaking the morphological and compositional symmetries of metallic nanoparticle (NP) dimers provides a novel approach to modulate plasmon coupling between the NPs. In this study, we...     

Symmetry Breaking in the Life Cycle of the Budding Yeast

The budding yeast Saccharomyces cerevisiae has been an invaluable model system for the study of the establishment of cellular asymmetry and growth polarity in response to specific physiological cues. A large body of experimental observations has shown that yeast cells are able to break symmetry and establish polarity through two coupled and partially redundant intrinsic mechanisms, even in the absence of any pre-existing external asymmetry. One of these mechanisms is dependent upon interplay between the actin cytoskeleton and the Rho family GTPase Cdc42, whereas the other relies on a Cdc42 GTPase signaling network. Integral to these mechanisms appear to be positive feedback loops capable of amplifying small and stochastic asymmetries. Spatial cues, such as bud scars and pheromone gradients, orient cell polarity by modulating the regulation of the Cdc42 GTPase cycle, thereby biasing the site of asymmetry amplification.The budding yeast Saccharomyces cerevisiae is a gift of nature, not just for its superb ability in fermentation to provide us food for hunger and pastime, but also for its relatively simple physiology, which has illuminated our understanding of many fundamental cellular processes. In particular, asymmetry is a way of life for the budding yeast, both when it grows vegetatively and initiates sexual reproductive cycles; as such, yeast has been an invaluable model for studying the establishment of cellular asymmetry. A haploid yeast cell in the G1 phase, which is round and grows isotropically, faces two options: to enter the mitotic cell cycle and grow a bud, or to refrain from cell cycle entry and form a mating projection (shmoo) toward a cell of the opposite mating type. In either case, the cell has to break symmetry to switch from isotropic growth to growth along a polarized axis (Fig. 1). These processes of cell polarity establishment are triggered either by internal signals from the cell cycle engine (budding) or by an external signal in the form of a pheromone gradient (mating).Open in a separate windowFigure 1.Symmetry breaking processes in the life cycle of budding yeast. Shown are the locations of actin patches, actin cables, and Cdc42 during polarized growth for both cycling cells and cells undergoing pheromone response. In G1 cells, Cdc42 is distributed symmetrically, and the actin cytoskeleton is not polarized. In response to cell cycle signals or mating pheromone stimulation, Cdc42 and the actin cytoskeleton become polarized: Cdc42 forms a “polar cap” and actin cables become oriented to allow for targeted secretion. Polarized growth further leads to formation of a bud (cell cycle signal) or formation of a mating projection (pheromone signal). Images represent GFP-Cdc42 (green), and rhodamine-phalloidin staining of filamentous actin (red).Pioneering work involving isolation and characterization of mutants deficient in various aspects of budding and shmoo formation identified key components of the molecular pathways underlying yeast polarized morphogenesis. Despite the relative simplicity of yeast, it has become increasingly clear that many of the genes that control the establishment of cell polarity are conserved between yeast and more complex eukaryotic organisms (see McCaffrey and Macara 2009; Munro and Bowerman 2009; Wang 2009; Nelson 2009). In particular, the small GTPase Cdc42, first discovered in yeast (Adams et al. 1990) and subsequently shown to be required for cell polarization in many eukaryotic organisms (Etienne-Manneville 2004), is the central regulator of yeast polarity.Common principles have begun to emerge to explain symmetry breaking under varying physiological conditions. One of these principles is the self-organizing nature of cell polarity. Whereas under physiological conditions yeast cells polarize toward an environmental asymmetry (pheromone gradient) or a “landmark,” i.e., the bud scar, deposited on the cell surface from a previous division (in a process called bud site selection), it is clear that the ability to undergo symmetry breaking to establish polarity in a random orientation is independent of these cues. It is tempting to speculate that the basic molecular machinery for symmetry breaking, which is required for asexual proliferation through budding, might have evolved independently of the machinery underlying mating and bud site selection.As in all polarized cell systems, yeast polarity is manifested as both an asymmetry in the distribution of signaling molecules and in the organization of the cytoskeleton. In yeast, the switch from an isotropic distribution of Cdc42 on the plasma membrane to a polarized distribution (Fig. 1) is required for the polarized organization of the actin cytoskeleton and membrane trafficking systems, and eventually orientated cell growth. Recent work also showed that the cytoskeleton and the membrane trafficking system can in turn impact the localization of Cdc42 and possibly other membrane‐associated regulatory molecules (Karpova et al. 2000; Wedlich-Soldner et al. 2004; Irazoqui et al. 2005; Zajac et al. 2005). A combination of experimental and theoretical analyses strongly suggests that the interplay between signaling and structural pathways is at the heart of the cell’s intrinsic ability to break symmetry.As there have been recent review articles on the polarized organization of budding yeast growth systems (Bretscher 2003; Pruyne et al. 2004b) and on the molecular parts list involved in cell polarization (Park and Bi 2007), this article is specifically focused on the mechanisms of symmetry breaking at two levels: first as a self-organization process accomplished through dynamic interplay between intrinsic signaling and cytoskeletal systems, which enables vegetative proliferation through bud formation; and second, as an adaptive process where polarity is spatially harnessed by physical cues that arise during bud-site selection and mating. Finally, we briefly extend our discussion to include the role of polarity in yeast aging and cell fate determination. This exciting, relatively new area of research has made important advances in our understanding of how asymmetry can be an important mechanism to ensure long-lasting fitness of a fast proliferating population.     

Where to Go: Breaking the Symmetry in Cell Motility

Cell migration in the “correct” direction is pivotal for many biological processes. Although most work is devoted to its molecular mechanisms, the cell’s preference for one direction over others, thus overcoming intrinsic random motility, epitomizes a profound principle that underlies all complex systems: the choice of one axis, in structure or motion, from a uniform or symmetric set of options. Explaining directional motility by an external chemo-attractant gradient does not solve but only shifts the problem of causation: whence the gradient? A new study in PLOS Biology shows cell migration in a self-generated gradient, offering an opportunity to take a broader look at the old dualism of extrinsic instruction versus intrinsic symmetry-breaking in cell biology.

When you come to a fork in the road, take it.–Yogi Berra 1925–2015

     

Disappearance of Plasmonically Induced Reflectance by Breaking Symmetry in Metamaterials

Although, using cut-out I-II and H-II structures, it has been proved that symmetry broken is necessitous to have a plasmonically induced reflectance (PIR) but it is also possible to create PIR effect in a symmetric cut-out H-II structure. In this paper, in addition to reaffirming the possibility of creating PIR effect in symmetric structure using I-II structure, it is also proved, for both the I-II and H-II structures, that the created PIR effect in symmetric case can be vanished by breaking the symmetry. The created PIR effect in the two I-II and H-II structures will be compared in different situations.     

In Silico Reconstitution of Actin-Based Symmetry Breaking and Motility

Eukaryotic cells assemble viscoelastic networks of crosslinked actin filaments to control their shape, mechanical properties, and motility. One important class of actin network is nucleated by the Arp2/3 complex and drives both membrane protrusion at the leading edge of motile cells and intracellular motility of pathogens such as Listeria monocytogenes. These networks can be reconstituted in vitro from purified components to drive the motility of spherical micron-sized beads. An Elastic Gel model has been successful in explaining how these networks break symmetry, but how they produce directed motile force has been less clear. We have combined numerical simulations with in vitro experiments to reconstitute the behavior of these motile actin networks in silico using an Accumulative Particle-Spring (APS) model that builds on the Elastic Gel model, and demonstrates simple intuitive mechanisms for both symmetry breaking and sustained motility. The APS model explains observed transitions between smooth and pulsatile motion as well as subtle variations in network architecture caused by differences in geometry and conditions. Our findings also explain sideways symmetry breaking and motility of elongated beads, and show that elastic recoil, though important for symmetry breaking and pulsatile motion, is not necessary for smooth directional motility. The APS model demonstrates how a small number of viscoelastic network parameters and construction rules suffice to recapture the complex behavior of motile actin networks. The fact that the model not only mirrors our in vitro observations, but also makes novel predictions that we confirm by experiment, suggests that the model captures much of the essence of actin-based motility in this system.     

Degenerate Coupled Mode Division and Superposition Under Symmetry Breaking

Resonances in micrometer metal cavity structures are very important for the interactions between materials and light. Three similar cavities connected with waveguides are investigated through the finite difference time domain (FDTD) method and the coupled mode theory. Two fundamental surface resonance modes are demonstrated in the two simple cavities separately. Then two simple cavities are combined to form the third cavity. The fundamental resonant modes couple positively or oppositely to form coupled-mode resonances in the combined cavity. When the combined cavity structures are symmetric, the coupled-mode resonances lead to two transmission peaks. While the symmetry is broken with tens of nanometers displacements, the transmission peaks convert to dips. It is believed the Q value variation of coupled-mode resonances plays a key role in the conversion. When the structure is symmetric, the coupled-mode resonances in the upper and lower parts of the cavity have the same Q value and are degenerate. The superposition of them leads transmission peaks. While the symmetry is broken, the Q values of resonances in the upper and lower part of the cavity are different, leading to the degenerate coupled mode division. The superposition of the different Q-factor modes leads to the dips. The sensitive variation to the symmetry of structures can be used to control light-material interactions, optical switch, and improve the sensitivity of sensor devices.

     

Symmetry Breaking in a Model of Antigenic Variation with Immune Delay

Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental equation for the eigenvalues. This allows one to identify periodic solutions with different symmetries arising at a Hopf bifurcation. In the case of small immune delay, the boundary of the Hopf bifurcation is found in a closed form in terms of system parameters. For arbitrary values of the time delay, general expressions for the critical time delay are found, which indicate bifurcation to an odd or even periodic solution. Numerical simulations of the full system are performed to illustrate different types of dynamical behaviour. The results of this analysis are quite generic and can be used to study within-host dynamics of many infectious diseases.