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Concept: Symmetry


While components of the pathway that establishes left-right asymmetry have been identified in diverse animals, from vertebrates to flies, it is striking that the genes involved in the first symmetry-breaking step remain wholly unknown in the most obviously chiral animals, the gastropod snails. Previously, research on snails was used to show that left-right signaling of Nodal, downstream of symmetry breaking, may be an ancestral feature of the Bilateria [1, 2]. Here, we report that a disabling mutation in one copy of a tandemly duplicated, diaphanous-related formin is perfectly associated with symmetry breaking in the pond snail. This is supported by the observation that an anti-formin drug treatment converts dextral snail embryos to a sinistral phenocopy, and in frogs, drug inhibition or overexpression by microinjection of formin has a chirality-randomizing effect in early (pre-cilia) embryos. Contrary to expectations based on existing models [3-5], we discovered asymmetric gene expression in 2- and 4-cell snail embryos, preceding morphological asymmetry. As the formin-actin filament has been shown to be part of an asymmetry-breaking switch in vitro [6, 7], together these results are consistent with the view that animals with diverse body plans may derive their asymmetries from the same intracellular chiral elements [8].

Concepts: DNA, Gene, Gene expression, Animal, Symmetry, Mollusca, Gastropod shell, Snail


Bilateral animals, including humans and most metazoans, are not perfectly symmetrical. Some internal structures are distributed asymmetrically to the right or left side. A conserved Nodal and BMP signaling system directs molecular pathways that impart the sidedness to those asymmetric structures. In the sea urchin embryo, one such asymmetrical structure, oddly enough, is the entire adult, which grows out of left sided structures produced in the larva. In a paper just published in PLOS Biology, BMP signaling is shown to be necessary early in larval development to initiate the asymmetric specification of one of those left-sided structures, called the left coelomic pouch. This study reports that BMP signaling activates a group of transcription factors asymmetrically in the left coelomic pouch only, which launch the pathway that eventually leads to the formation of the adult that emerges from the larva at metamorphosis.

Concepts: Insect, Developmental biology, Larva, Animal, Mesoderm, Symmetry, Metamorphosis, Asymmetry


Human artefacts in general are highly structured and often display ordering principles such as translational, reflectional or rotational symmetry. In contrast, human artefacts that are intended to appear random and non symmetrical are very rare. Furthermore, many studies show that humans find it extremely difficult to recognize or reproduce truly random patterns or sequences. Here, we attempt to model two-dimensional decorative spatial patterns produced by humans that show no obvious order. “Crazy quilts” represent a historically important style of quilt making that became popular in the 1870s, and lasted about 50 years. Crazy quilts are unusual because unlike most human artefacts, they are specifically intended to appear haphazard and unstructured. We evaluate the degree to which this intention was achieved by using statistical techniques of spatial point pattern analysis to compare crazy quilts with regular quilts from the same region and era and to evaluate the fit of various random distributions to these two quilt classes. We found that the two quilt categories exhibit fundamentally different spatial characteristics: The patch areas of crazy quilts derive from a continuous random distribution, while area distributions of regular quilts consist of Gaussian mixtures. These Gaussian mixtures derive from regular pattern motifs that are repeated and we suggest that such a mixture is a distinctive signature of human-made visual patterns. In contrast, the distribution found in crazy quilts is shared with many other naturally occurring spatial patterns. Centroids of patches in the two quilt classes are spaced differently and in general, crazy quilts but not regular quilts are well-fitted by a random Strauss process. These results indicate that, within the constraints of the quilt format, Victorian quilters indeed achieved their goal of generating random structures.

Concepts: Statistics, Symmetry, Mixture, Pattern, Rotational symmetry, Pattern matching, Quilting, Quilt


Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.

Concepts: Statistics, Mathematics, Symmetry, Estimation, Symmetry group, Rotational symmetry, Point groups in three dimensions, Reflection symmetry


Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterized by mesoscale turbulence, which is the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organizes into a spin state where neighboring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elastic effects. Our virtual prototype demonstrates a new research direction for the design of micromachines powered by the nematohydrodynamic properties of active turbulence.

Concepts: Fluid dynamics, Symmetry, Group, Fluid, Standard Model, Symmetry group, Spontaneous symmetry breaking, Higgs mechanism


Interactions between individuals and the structure of their environment play a crucial role in shaping self-organized collective behaviors. Recent studies have shown that ants crossing asymmetrical bifurcations in a network of galleries tend to follow the branch that deviates the least from their incoming direction. At the collective level, the combination of this tendency and the pheromone-based recruitment results in a greater likelihood of selecting the shortest path between the colony’s nest and a food source in a network containing asymmetrical bifurcations. It was not clear however what the origin of this behavioral bias is. Here we propose that it results from a simple interaction between the behavior of the ants and the geometry of the network, and that it does not require the ability to measure the angle of the bifurcation. We tested this hypothesis using groups of ant-like robots whose perceptual and cognitive abilities can be fully specified. We programmed them only to lay down and follow light trails, avoid obstacles and move according to a correlated random walk, but not to use more sophisticated orientation methods. We recorded the behavior of the robots in networks of galleries presenting either only symmetrical bifurcations or a combination of symmetrical and asymmetrical bifurcations. Individual robots displayed the same pattern of branch choice as individual ants when crossing a bifurcation, suggesting that ants do not actually measure the geometry of the bifurcations when travelling along a pheromone trail. Finally at the collective level, the group of robots was more likely to select one of the possible shorter paths between two designated areas when moving in an asymmetrical network, as observed in ants. This study reveals the importance of the shape of trail networks for foraging in ants and emphasizes the underestimated role of the geometrical properties of transportation networks in general.

Concepts: Psychology, Cognition, Symmetry, Geometry, Behavior, Human behavior, Behaviorism, Robot


Although broadly admired for its aesthetic qualities, the art of origami is now being recognized also as a framework for mechanical metamaterial design. Working with the Miura-ori tessellation, we find that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned. By virtue of their interactions, these mechanically stable lattice defects also lead to emergent crystallographic structures such as vacancies, dislocations, and grain boundaries. Each of these structures comes from an arrangement of reversible folds, highlighting a connection between mechanical metamaterials and programmable matter. Given origami’s scale-free geometric character, this framework for metamaterial design can be directly transferred to milli-, micro-, and nanometer-size systems.

Concepts: Crystal structure, Crystallography, Symmetry, Materials science, Crystal system, Crystallographic defect, Origami, Crease pattern


Humans can use hand tools smoothly and effectively in varying circumstances; in other words, skillfully. A few other species of primates crack encased foods using hammer tools and anvils. Are they skilled? Positioning the food on the anvil so that it does not fall off when struck is a component of skilled cracking. We discovered that bearded capuchin monkeys deliberately place palm nuts in a relatively stable position on the anvil before striking them. In the first experiment, we marked the meridians of palm nuts where they stopped when rolled on a flat surface (“Stop meridian”). We videotaped monkeys as they cracked these nuts on an anvil. In playback we coded the position of the Stop meridian prior to each strike. Monkeys typically knocked the nuts on the anvil a few times before releasing them in a pit. They positioned the nuts so that the Stop meridian was within 30 degrees of vertical with respect to gravity more often than expected, and the nuts rarely moved after the monkeys released them. In the second experiment, 14 blindfolded people (7 men) asked to position marked nuts on an anvil as if to crack them reliably placed them with the Stop meridian in the same position as the monkeys did. In the third experiment, two people judged that palm nuts are most bilaterally symmetric along a meridian on, or close to, the Stop meridian. Thus the monkeys reliably placed the more symmetrical side of the nuts against the side of the pit, and the nuts reliably remained stationary when released. Monkeys apparently used information gained from knocking the nut to achieve this position. Thus, monkeys place the nuts skillfully, strategically managing the fit between the variable nuts and pits in the anvil, and skilled placement depends upon information generated by manual action.

Concepts: Symmetry, Primate, Learning, Leadership, Capuchin monkey, Strike action


The tessellation of the Euclidean plane by regular polygons has been contemplated since ancient times and presents intriguing aspects embracing mathematics, art, and crystallography. Significant efforts were devoted to engineer specific 2D interfacial tessellations at the molecular level, but periodic patterns with distinct five-vertex motifs remained elusive. Here, we report a direct scanning tunneling microscopy investigation on the cerium-directed assembly of linear polyphenyl molecular linkers with terminal carbonitrile groups on a smooth Ag(111) noble-metal surface. We demonstrate the spontaneous formation of fivefold Ce-ligand coordination motifs, which are planar and flexible, such that vertices connecting simultaneously trigonal and square polygons can be expressed. By tuning the concentration and the stoichiometric ratio of rare-earth metal centers to ligands, a hierarchic assembly with dodecameric units and a surface-confined metal-organic coordination network yielding the semiregular Archimedean snub square tiling could be fabricated.

Concepts: Symmetry, Polyhedron, Tessellation, Polytope, Hexagon, Regular polygon, Tiling, Tiling by regular polygons


Restricting our scope to the dynamical motion of the leaflets, we present a computational model for a symmetric, tri-leaflet, bioprosthetic heart valve (BHV) at the end of five complete cardiac pressure cycles, reaching the steady state of deformation during both closing and opening phases. To this end, we utilized a highly anisotropic material model for the large deformation behavior of the tissue material, for which an experimental validation was provided. The important findings are: (1) material anisotropy has significant effect on the valve opening/closing; (2) the asymmetric deformations, especially in the fully closed configuration, justify the use of cyclic symmetry; (3) adopting the fully-open position as an initial/reference configuration has the advantage of completely bypassing any complications arising from the need to assume the size and shape of the contact area in the coaptation regions of the leaflets that is necessary when the alternative, commonly-used, approach of selecting the fully-closed position is used as a reference; and (4) with proper treatments for both material anisotropy and tissue-to-tissue contact, the overall BHV model provide realistic results in conformity with the ex vivo/in vitro experiments.

Concepts: Thermodynamics, Symmetry, Geometry, Young's modulus, Attractor, Artificial heart valve, Asymmetry, Point groups in three dimensions