Declaration For Greater Independence

Symmetry in Biology

In biology, (symmetry refers to) the repetition of the parts in an animal or plant in an orderly fashion.

Specifically, symmetry refers to a correspondence of body parts, in size, shape, and relative position, on opposite sides of a dividing line or distributed around a central point or axis. With the exception of radial symmetry, external form has little relation to internal anatomy, since animals of very different anatomical construction may have the same type of symmetry.

Certain animals, particularly most sponges and the ameboid protozoans, lack symmetry, having either an irregular shape different for each individual or else one undergoing constant changes of form. The vast majority of animals, however, exhibit a definite symmetrical form. Four such patterns of symmetry occur among animals: spherical, radial, biradial, and bilateral.

In spherical symmetry, illustrated only by the protozoan groups Radiolaria and Heliozoia, the body has the shape of a sphere and the parts are arranged concentrically around or radiate from the centre of the sphere. Such an animal has no ends or sides, and any plane passing through the centre will divide the animal into equivalent halves. The spherical type of symmetry is possible only in minute animals of simple internal construction, since in spheres the interior mass is large relative to the surface area and becomes too large for efficient functioning with increase in size and complexity.

In radial symmetry the body has the general form of a short or long cylinder or bowl, with a central axis from which the body parts radiate or along which they are arranged in regular fashion. The main axis is heteropolar—i.e., with unlike ends, one of which bears the mouth and is termed the oral, or anterior, end, and the other of which, called the aboral, or posterior, end, forms the rear end of the animal and may bear the anus. The main axis is hence termed the oral-aboral, or anteroposterior, axis. Except in animals having an odd number of parts arranged in circular fashion (as in the five-armed starfishes), any plane passing through this axis will divide the animal into symmetrical halves. Animals having three, five, seven, etc., parts in a circle have symmetry that may be referred to, respectively, as three-rayed, five-rayed, seven-rayed, etc.; only certain planes through the axis will divide such animals into symmetrical halves. Radial symmetry is found in the coelenterates and echinoderms.

In biradial symmetry, in addition to the anteroposterior axis, there are also two other axes or planes of symmetry at right angles to it and to each other: the sagittal, or median vertical-longitudinal, and transverse, or cross, axes. Such an animal therefore not only has two ends but also has two pairs of symmetrical sides. There are but two planes of symmetry in a biradial animal, one passing through the anteroposterior and sagittal axes and the other through the anteroposterior and transverse axes. Biradial symmetry occurs in the comb jellies.

In bilateral symmetry there are the same three axes as in biradial symmetry but only one pair of symmetrical sides, the lateral sides, since the other two sides, called the dorsal (back) and ventral (belly) surfaces, are unlike. Thus, only one plane of symmetry will divide a bilateral animal into symmetrical halves, the median longitudinal, or sagittal, plane. Bilateral symmetry is characteristic of the vast majority of animals, including insects, fishes, amphibians, reptiles, birds, mammals, and most crustaceans.

The concept of symmetry is also applied in botany. A flower is considered symmetrical when each whorl consists of an equal number of parts or when the parts of any one whorl are multiples of that preceding it. Thus, a symmetrical flower may have five sepals, five petals, five stamens, and five carpels, or the number of any of these parts may be a multiple of five.

The number of parts in the pistillate whorl is frequently not in conformity with that in the other whorls, but in such cases the flower is still called symmetrical, provided that the other whorls are normal. A flower in which the parts are in twos is dimerous; in threes, fours, or fives, (trimerous, tetramerous, or pentamerous), respectively. Trimerous symmetry is the rule in the monocotyledons, pentamerous the most common in the dicotyledons, although dimerous and tetramerous flowers also occur in the latter group.

When the different members of each whorl are alike, the flower is regular and is referred to as actinomorphic, or radially symmetrical, as in the petunia, buttercup, and wild rose. Differences in size or shape of the parts of a whorl make the flower irregular (as in the canna and Asiatic dayflower). When a flower can be divided by a single plane into two equal parts, it is zygomorphic, or bilaterally symmetrical, as in the snapdragon, orchid, and sweet pea.

Crystals

Crystals form the basis of many skeletons, such as the calcareous triradiate (three-armed) and quadradiate (four-armed) spicules of calcareous sponges. The cellular components of the body of the sponge usually are not rigid and have no fixed continuity; cells from the outer, inner, and middle layers of a sponge are freely mobile. Spicules, which may be of silica, often extend far from the body. They can be shed at times and replaced by new spicules. Skeletal fibres are present in many sponges.

Calcareous spicules, large and small, form an important part of the skeleton of many coelenterates. Huge needlelike spicules, projecting beyond the soft tissue of sea pens (pennatulids), for example, both support the flanges that bear feeding polyps and hinder browsing by predators. Minute internal spicules may be jammed together to form a skeletal axis, as in the red coral. In some corals (Alcyonaria), spicules combine with fibres made of keratin (a protein also found in hair and feathers) or keratins with amorphous calcite (noncrystalline calcium carbonate) to form axial structures of great strength and size, enabling colonies to reach large bushlike proportions.

Skeletons consisting of cuticle but remote from the body surface give support and protection to other coelenterates, the colonial sedentary hydroids, and form tubes in which pogonophores (small threadlike aquatic animals) live. Exoskeletons that are superficially similar but quite different from hydroids and pogonophores in both manner of growth and internal support occur in the graptolites, an extinct group, and in the protochordates, Rhabdopleura and Cephalodiscus. Some graptolites, known only from fossil skeletal remains many millions of years old, had skeletons similar to those of Rhabdopleura.

In segmented and in many nonsegmented invertebrates, cuticle is secreted by the ectoderm and remains in contact with it. It is thin in annelid worms (e.g., the earthworm) and thicker in roundworms (nematodes) and arthropods. In many arthropods the cuticle is infolded to form endoskeletal structures of considerable complexity. Rigidity is imposed on parts of the cuticle of arthropods either by sclerotization or tanning, a process involving dehydration (as in crustaceans and insects), by calcification (as in millipedes), or by both, as in many crabs. In most arthropods the body and legs are clearly segmented. On the dorsal (upper) side of each segment is a so-called tergal sclerite of calcified or sclerotized cuticle, usually a ventral (lower) sternite and often lateral pleurites—i.e., side plates. There may be much fusion of sclerites on the same segment. Sometimes fusion occurs between dorsal sclerites of successive segments, to form rigid plates. Leg sclerotizations are usually cylindrical.

Internally, apodemes are hollow rods or flanges derived from the cuticle; they extend inward from the exoskeleton. Apodemes have a function similar to the bones of vertebrates, for they provide sites for muscle insertion, thereby allowing the leverage that can cause movement of other parts of the skeleton independent of hydrostatic forces. The apodemal system is most fully developed in the larger and more swiftly moving arthropods. The cuticle is a dead secretion and can only increase in thickness. At intervals an arthropod molts the entire cuticle, pulling out the apodemes. The soft body rapidly swells before secreting a new, stiff cuticle. The molting process limits the upper size of cuticle-bearing animals. Arthropods can never achieve the body size of the larger vertebrates, in which the bones grow with the body, because the mechanical difficulties of molting would be too great. The mechanical properties of bone limit terrestrial mammals to about the size of a 12-ton elephant. In water, however, bone can support a heavier animal, such as a blue whale weighing 100 tons. Bone is mechanically unsuited to support an animal as bulky as, for example, a large ship.

Semirigid structures

Flexible cuticular structures on the surface of unsegmented roundworms and arthropods are just as important in providing support as are the more rigid sclerites. Mobility between the sclerites of body and legs is maintained by regions of flexible cuticle, the arthrodial membranes. Some sclerites are stiffened by closely packed cones of sclerotization at their margins, forming structures that combine rigidity and flexibility.

Symmetry in Crystallography

In crystallography, (symmetry is the) fundamental property of the orderly arrangements of atoms found in crystalline solids. Each arrangement of atoms has a certain number of elements of symmetry; i.e., changes in the orientation of the arrangement of atoms seem to leave the atoms unmoved. One such element of symmetry is rotation; other elements are translation, reflection, and inversion. The elements of symmetry present in a particular crystalline solid determine its shape and affect its physical properties.

Translations involve displacement of the crystal in a direction that replaces each atom by one of its identical neighbours, so that the atoms seem unmoved. Rotations turn the crystal around an axis of symmetry passing through the crystal; the only rotations compatible with translational symmetry move the crystal through an angle of 360° divided by n, with n equal to 1, 2, 3, 4, or 6. Reflections exchange the parts of the crystal on the two sides of a plane of symmetry (mirror plane) within the solid. Inversions move every atom to another position in the crystal; the old and new positions of the atom lie upon a line, at the middle of which is the centre of inversion. So-called improper rotations are rotations followed by reflections (known as roto-reflections) or rotations followed by inversions (called rotoinversions).

A crystal can be classified according to its elements of symmetry; for example, it may belong to one of 230 space groups, 32 point groups, 14 Bravais lattices, and 7 crystal systems. A crystal can be represented diagrammatically by an orderly stacking of unit cells; the shape of the unit cell determines which of the seven crystal systems the crystal belongs to. Unit cells of the same shape may have points (each representing an atom or a group of atoms) at their centres or on their faces, in addition to those at their corners. These additional lattice points divide the 7 crystal systems into 14 Bravais lattices; the Bravais lattices are subdivided into 32 crystal classes, or point groups. Each point group corresponds to one of the possible combinations of rotations, reflections, inversions, and improper rotations; with the inclusion of translational elements, 230 space groups are produced.

Quasi-Crystal (also called quasi-periodic crystal)

(Quasicrystal is) matter formed atomically in a manner somewhere between the amorphous solids of glasses (special forms of metals and other minerals, as well as common glass) and the precise pattern of crystals. Like crystals, quasicrystals contain an ordered structure, but the patterns are subtle and do not recur at precisely regular intervals. Rather, quasicrystals appear to be formed from two different structures assembled in a non-repeating array, the three-dimensional equivalent of a tile floor made from two shapes of tile and having an orientational order but no repetition.

Although when first discovered such structures surprised the scientific community, it now appears that quasicrystals rank among the most common structures in alloys of aluminum with such metals as iron, cobalt, or nickel. While no major commercial applications yet exploit properties of the quasicrystalline state directly, quasicrystals form in compounds noted for their high strength and light weight, suggesting potential applications in aerospace and other industries.