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

     

Baculovirus Actin-Based Motility Drives Nuclear Envelope Disruption and Nuclear Egress

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Hidden Chromosome Symmetry: In Silico Transformation Reveals Symmetry in 2D DNA Walk Trajectories of 671 Chromosomes

Maps of 2D DNA walk of 671 examined chromosomes show composition complexity change from symmetrical half-turn in bacteria to pseudo-random trajectories in archaea, fungi and humans. In silico transformation of gene order and strand position returns most of the analyzed chromosomes to a symmetrical bacterial-like state with one transition point. The transformed chromosomal sequences also reveal remarkable segmental compositional symmetry between regions from different strands located equidistantly from the transition point. Despite extensive chromosome rearrangement the relation of gene numbers on opposite strands for chromosomes of different taxa varies in narrow limits around unity with Pearson coefficient r = 0.98. Similar relation is observed for total genes'' length (r = 0.86) and cumulative GC (r = 0.95) and AT (r = 0.97) skews. This is also true for human coding sequences (CDS), which comprise only several percent of the entire chromosome length. We found that frequency distributions of the length of gene clusters, continuously located on the same strand, have close values for both strands. Eukaryotic gene distribution is believed to be non-random. Contribution of different subsystems to the noted symmetries and distributions, and evolutionary aspects of symmetry are discussed.     

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     

Rickettsia Actin-Based Motility Occurs in Distinct Phases Mediated by Different Actin Nucleators

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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.     

Cellular Morphogenesis In Silico

We describe a model that simulates spherical cells of different types that can migrate and interact either attractively or repulsively. We find that both expected morphologies and previously unreported patterns spontaneously self-assemble. Among the newly discovered patterns are a segmented state of alternating discs, and a “shish-kebab” state, in which one cell type forms a ring around a second type. We show that these unique states result from cellular attraction that increases with distance (e.g., as membranes stretch viscoelastically), and would not be seen in traditional, e.g., molecular, potentials that diminish with distance. Most of the states found computationally have been observed in vitro, and it remains to be established what role these self-assembled states may play in in vivo morphogenesis.     

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.     

Gravitational Symmetry Breaking Leads to a Polar Liquid Crystal Phase of Microtubules In Vitro

Recent space-flight experiments performed by Tabony's team provided further evidence that a microgravity environment strongly affects the spatio-temporal organization of microtubule assemblies. Characteristic time and length scales were found that govern the organization of oriented bundles under Earth's gravitational field (GF). No such organization has been observed in a microgravity environment. This paper discusses physical mechanisms resulting in pattern formation under gravity and its disappearance in microgravity. The subtle interplay between chemical kinetics, diffusion, gravitational drift, thermal fluctuations, electrostatic interactions and liquid crystalline characteristics provides a plausible scenario.     

Dual Symmetry Breaking in Gold-Silica-Gold Multilayer Nanoshells

In this study, the optical properties induced by dual symmetry breaking including both shell cutting and core offsetting in the gold-silica-gold multilayer nanoshells have been studied by the discrete dipole approximation simulations and the plasmon hybridization theory. The influences of the incident polarization and geometrical parameters on the plasmon resonances of these dual-symmetry-breaking Au-silica-Au multilayer nanoshells (DSMNS) are investigated. Under the combined effect of the two types of symmetry breaking, it is found that the polarization-dependent multiple plasmon resonances can be induced in the DSMNS. By changing the polarization of 90^o, the switching of the two transparency windows can be flexibly adjusted in the DSMNS with different types of Au core offsetting. This polarization-controlled transparency is likely to generate a wide range of photonic applications such as filters and color displays. Furthermore, the local refractive index sensitivity of the DSMNS is also investigated, and the triple extinction peaks simultaneous shift is found as the surrounding medium changed, which suggests the potential applications for biological sensors.     

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.     

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.

     

In Vitro Reconstitution of Microtubule Plus End-directed, GTPγS-sensitive Motility of Golgi Membranes

Purified Golgi membranes were mixed with cytosol and microtubules (MTs) and observed by video enhanced light microscopy. Initially, the membranes appeared as vesicles that moved along MTs. As time progressed, vesicles formed aggregates from which membrane tubules emerged, traveled along MTs, and eventually generated extensive reticular networks. Membrane motility required ATP, occurred mainly toward MT plus ends, and was inhibited almost completely by the H1 monoclonal antibody to kinesin heavy chain, 5′-adenylylimidodiphosphate, and 100 μM but not 20 μM vanadate. Motility was also blocked by GTPγS or AlF₄⁻ but was insensitive to AlCl₃, NaF, staurosporin, or okadaic acid. The targets for GTPγS and AlF₄⁻ were evidently of cytosolic origin, did not include kinesin or MTs, and were insensitive to several probes for trimeric G proteins. Transport of Golgi membranes along MTs mediated by a kinesin has thus been reconstituted in vitro. The motility is regulated by one or more cytosolic GTPases but not by protein kinases or phosphatases that are inhibited by staurosporin or okadaic acid, respectively. The pertinent GTPases are likely to be small G proteins or possibly dynamin. The in vitro motility may correspond to Golgi-to-ER or Golgi-to-cell surface transport in vivo.     

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.