Symmetry in biology

Organisms with radial symmetry show a repeating pattern around a central axis such that they can be separated into several identical pieces when cut through the central point, much like pieces of a pie. Typically, this involves repeating a body part 4, 5, 6 or 8 times around the axis – referred to as tetramerism, pentamerism, hexamerism and octamerism, respectively. Such organisms exhibit no left or right sides but do have a top and a bottom surface, or a front and a back.

George Cuvier classified animals with radial symmetry in the taxon Radiata (Zoophytes),[5][4] which is now generally accepted to be an assemblage of different animal phyla that do not share a single common ancestor (a polyphyletic group).[6] Most radially symmetric animals are symmetrical about an axis extending from the center of the oral surface, which contains the mouth, to the center of the opposite (aboral) end. Animals in the phyla Cnidaria and Echinodermata generally show radial symmetry,[7] although many sea anemones and some corals within the Cnidaria have bilateral symmetry defined by a single structure, the siphonoglyph.[8] Radial symmetry is especially suitable for sessile animals such as the sea anemone, floating animals such as jellyfish, and slow moving organisms such as starfish; whereas bilateral symmetry favours locomotion by generating a streamlined body.

Many flowers are also radially symmetric, or "actinomorphic". Roughly identical floral structures – petals, sepals, and stamens – occur at regular intervals around the axis of the flower, which is often the female reproductive organ containing the carpel, style and stigma.[9]

Lilium bulbiferum displays hexamerism with repeated parts arranged around the axis of the flower.

Subtypes of radial symmetry

Some jellyfish, such as Aurelia marginalis, show tetramerism with a four-fold radial symmetry. This is immediately obvious when looking at the jellyfish due to the presence of four gonads, visible through its translucent body. This radial symmetry is ecologically important in allowing the jellyfish to detect and respond to stimuli (mainly food and danger) from all directions.

Apple cut horizontally showing that pentamerism also occurs in fruit

Flowering plants show five-fold symmetry, or pentamerism, in many of their flowers and fruits. This is easily seen through the arrangement of five carpels (seed pockets) in an apple when cut transversely. Among animals, only the echinoderms such as sea stars, sea urchins, and sea lilies are pentamerous as adults, with five arms arranged around the mouth. Being bilaterian animals, however, they initially develop with mirror symmetry as larvae, then gain pentaradial symmetry later.[10]

Hexamerism is found in the corals and sea anemones (class Anthozoa), which are divided into two groups based on their symmetry. The most common corals in the subclass Hexacorallia have a hexameric body plan; their polyps have six-fold internal symmetry and a number of tentacles that is a multiple of six.

Octamerism is found in corals of the subclass Octocorallia. These have polyps with eight tentacles and octameric radial symmetry. The octopus, however, has bilateral symmetry, despite its eight arms.

Triradial symmetry was present in Trilobozoa from the Late Ediacaran period.

Gastroenteritis viruses have icosahedral symmetry

Icosahedral symmetry occurs in an organism which contains 60 subunits generated by 20 faces, each an equilateral triangle, and 12 corners. Within the icosahedron there is 2-fold, 3-fold and 5-fold symmetry. Many viruses, including canine parvovirus, show this form of symmetry due to the presence of an icosahedral viral shell. Such symmetry has evolved because it allows the viral particle to be built up of repetitive subunits consisting of a limited number of structural proteins (encoded by viral genes), thereby saving space in the viral genome. The icosahedral symmetry can still be maintained with more than 60 subunits, but only in factors of 60. For example, the T=3 Tomato bushy stunt virus has 60x3 protein subunits (180 copies of the same structural protein).[11][12] Although these viruses are often referred to as 'spherical', they do not show true mathematical spherical symmetry.

In the early 20th century, Ernst Haeckel described (Haeckel, 1904) a number of species of Radiolaria, some of whose skeletons are shaped like various regular polyhedra. Examples include Circoporus octahedrus, Circogonia icosahedra, Lithocubus geometricus and Circorrhegma dodecahedra. The shapes of these creatures should be obvious from their names. Tetrahedral symmetry is not present in Callimitra agnesae.

Volvox is a microscopic green freshwater alga with spherical symmetry. Young colonies can be seen inside the larger ones.

Spherical symmetry is characterised by the ability to draw an endless, or great but finite, number of symmetry axes through the body. This means that spherical symmetry occurs in an organism if it is able to be cut into two identical halves through any cut that runs through the organism's center. True spherical symmetry is not found in animal body plans.[1] Organisms which show approximate spherical symmetry include the freshwater green alga Volvox.[7]

Bacteria are often referred to as having a 'spherical' shape. Bacteria are categorized based on their shapes into three classes: cocci (spherical-shaped), bacillus (rod-shaped) and spirochetes (spiral-shaped) cells. In reality, this is a severe over-simplification as bacterial cells can be curved, bent, flattened, oblong spheroids and many more shapes.[13] Due to the huge number of bacteria considered to be cocci (coccus if a single cell), it is unlikely that all of these show true spherical symmetry. It is important to distinguish between the generalized use of the word 'spherical' to describe organisms at ease, and the true meaning of spherical symmetry. The same situation is seen in the description of viruses – 'spherical' viruses do not necessarily show spherical symmetry, being usually icosahedral.

Organisms with bilateral symmetry contain a single plane of symmetry, the sagittal plane, which divides the organism into two roughly mirror image left and right halves – approximate reflectional symmetry.

The small emperor moth, Saturnia pavonia, displays a deimatic pattern with bilateral symmetry.

Flower of bee orchid (Ophrys apifera) is bilaterally symmetrical (zygomorphic). The lip of the flower resembles the (bilaterally symmetric) abdomen of a female bee; pollination occurs when a male bee attempts to mate with it.

Animals with bilateral symmetry are classified into a large group called the bilateria which contains 99% of all animals (comprising over 32 phyla and 1 million described species). All bilaterians have some asymmetrical features; for example, the human heart and liver are positioned asymmetrically despite the body having external bilateral symmetry.[14]

The bilateral symmetry of bilaterians is a complex trait which develops due to the expression of many genes. The bilateria have two axes of polarity. The first is an anterior-posterior (AP) axis which can be visualised as an imaginary axis running from the head or mouth to the tail or other end of an organism. The second is the dorsal-ventral (DV) axis which runs perpendicular to the AP axis.[15][1] During development the AP axis is always specified before the DV axis[16] which is known as the second embryonic axis. The AP axis is essential in defining the polarity of bilateria and allowing the development of a front and back to give the organism direction. The front end encounters the environment before the rest of the body so sensory organs such as eyes tend to be clustered there. This is also the site where a mouth develops since it is the first part of the body to encounter food. Therefore, a distinct head, with sense organs connected to a central nervous system, tends to develop.[17] This pattern of development (with a distinct head and tail) is called cephalization. It is also argued that the development of an AP axis is important in locomotion – bilateral symmetry gives the body an intrinsic direction and allows streamlining to reduce drag.

In addition to animals, the flowers of some plants also show bilateral symmetry. Such plants are referred to as zygomorphic and include the orchid (Orchidaceae) and pea (Fabaceae) families, and most of the figwort family (Scrophulariaceae).[18][19] The leaves of plants also commonly show approximate bilateral symmetry.

Biradial symmetry is found in organisms which show morphological features (internal or external) of both bilateral and radial symmetry. Unlike radially symmetrical organisms which can be divided equally along many planes, biradial organisms can only be cut equally along two planes. This could represent an intermediate stage in the evolution of bilateral symmetry from a radially symmetric ancestor.[20]

The animal group with the most obvious biradial symmetry is the ctenophores. In ctenophores the two planes of symmetry are (1) the plane of the tentacles and (2) the plane of the pharynx.[1] In addition to this group, evidence for biradial symmetry has even been found in the 'perfectly radial' freshwater polyp Hydra (a cnidarian). Biradial symmetry, especially when considering both internal and external features, is more common than originally accounted for.[21]

Like all the traits of organisms, symmetry (or indeed asymmetry) evolves due to an advantage to the organism – a process of natural selection. This involves changes in the frequency of symmetry-related genes throughout time.

Although asymmetry is typically associated with being unfit, some species have evolved to be asymmetrical as an important adaptation. Many members of the phylum Porifera (sponges) have no symmetry, though some are radially symmetric.[28]

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  Head of a male crossbill showing asymmetrical upper and lower beak
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  A winter flounder, a type of flatfish, with both eyes on the same side of its head
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  Hermit crabs have different sized claws
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  A Roman snail and its helical shell
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  Chicoreus palmarosae, a sea snail, illustrating asymmetry, which is seen in all gastropods in the form of a helical shell
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  A red slug, clearly showing the pneumostome
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  Male caribou usually possess one brow tine flattened into a shovel shape[35]

Symmetry breaking

The presence of these asymmetrical features requires a process of symmetry breaking during development, both in plants and animals. Symmetry breaking occurs at several different levels in order to generate the anatomical asymmetry which we observe. These levels include asymmetric gene expression, protein expression, and activity of cells.

For example, left-right asymmetry in mammals has been investigated extensively in the embryos of mice. Such studies have led to support for the nodal flow hypothesis. In a region of the embryo referred to as the node there are small hair-like structures (monocilia) which all rotate together in a particular direction. This creates a unidirectional flow of signalling molecules causing these signals to accumulate on one side of the embryo and not the other. This results in the activation of different developmental pathways on each side, and subsequent asymmetry.[36][37]

Schematic diagram of signalling pathways on the left and right side of a chick embryo, ultimately leading to the development of asymmetry

Much of the investigation of the genetic basis of symmetry breaking has been done on chick embryos. In chick embryos the left side expresses genes called NODAL and LEFTY2 which activate PITX2 to signal the development of left side structures. Whereas, the right side does not express PITX2 and consequently develops right side structures.[38][39] A more complete pathway is shown in the image at the side of the page.

For more information about symmetry breaking in animals please refer to the left-right asymmetry page.

Plants also show asymmetry. For example the direction of helical growth in Arabidopsis, the most commonly studied model plant, shows left-handedness. Interestingly, the genes involved in this asymmetry are similar (closely related) to those in animal asymmetry – both LEFTY1 and LEFTY2 play a role. In the same way as animals, symmetry breaking in plants can occur at a molecular (genes/proteins), subcellular, cellular, tissue and organ level.[40]