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Chirality is a property of
asymmetry Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in pre ...
important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from its
mirror image A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical effect it results from reflection off from substance ...
; that is, it cannot be
superimposed Superimposition is the placement of one thing over another, typically so that both are still evident. Graphics In graphics, superimposition is the placement of an image or video on top of an already-existing image or video, usually to add to t ...
onto it. Conversely, a mirror image of an ''achiral'' object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called ''enantiomorphs'' (Greek, "opposite forms") or, when referring to molecules, '' enantiomers''. A non-chiral object is called ''achiral'' (sometimes also ''amphichiral'') and can be superposed on its mirror image. The term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894: Human
hand A hand is a prehensile, multi-fingered appendage located at the end of the forearm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs. A few other vertebrates such as the koala (which has two opposable thumbs on each "h ...
s are perhaps the most recognized example of chirality. The left hand is a non-superimposable mirror image of the right hand; no matter how the two hands are oriented, it is impossible for all the major features of both hands to coincide across all axes.Georges Henry Wagnière, ''On Chirality and the Universal Asymmetry: Reflections on Image and Mirror Image'' (2007). This difference in symmetry becomes obvious if someone attempts to shake the right hand of a person using their left hand, or if a left-handed glove is placed on a right hand. In mathematics, ''chirality'' is the property of a figure that is not identical to its mirror image.


Mathematics

In
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a figure is chiral (and said to have chirality) if it cannot be mapped to its mirror image by
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
s and
translation Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
s alone. For example, a right shoe is different from a left shoe, and clockwise is different from anticlockwise. See for a full mathematical definition. A chiral object and its mirror image are said to be enantiomorphs. The word ''enantiomorph'' stems from the Greek (enantios) 'opposite' + (morphe) 'form'. A non-chiral figure is called achiral or amphichiral. The helix (and by extension a spun string, a screw, a propeller, etc.) and
Möbius strip In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and A ...
are chiral two-dimensional objects in three-dimensional ambient space. The J, L, S and Z-shaped ''
tetromino A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). Tetrominoes, like dominoes and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracu ...
es'' of the popular video game Tetris also exhibit chirality, but only in a two-dimensional space. Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves, glasses (sometimes), and shoes. A similar notion of chirality is considered in knot theory, as explained below. Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule.


Geometry

In
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a figure is achiral if — and only if — its
symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the amb ...
contains at least one ''orientation-reversing'' isometry. In two dimensions, every figure that possesses an
axis of symmetry Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.
is achiral, and it can be shown that every ''bounded'' achiral figure must have an axis of symmetry. In three dimensions, every figure that possesses a plane of symmetry or a center of symmetry is achiral. There are, however, achiral figures lacking both plane and center of symmetry. In terms of point groups, all chiral figures lack an improper axis of rotation (Sn). This means that they cannot contain a center of inversion (i) or a mirror plane (σ). Only figures with a point group designation of C1, Cn, Dn, T, O, or I can be chiral.


Knot theory

A
knot A knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a ''hitch'' fastens a rope to another object; a ...
is called
achiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from i ...
if it can be continuously deformed into its mirror image, otherwise it is called chiral. For example, the unknot and the figure-eight knot are achiral, whereas the
trefoil knot In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest k ...
is chiral.


Physics

In physics, chirality may be found in the spin of a particle, where the handedness of the object is determined by the direction in which the particle spins. Not to be confused with helicity, which is the projection of the spin along the linear momentum of a subatomic particle, chirality is an intrinsic quantum mechanical property, like spin. Although both chirality and helicity can have left-handed or right-handed properties, only in the massless case are they identical. In particular for a massless particle the helicity is the same as the chirality while for an antiparticle they have opposite sign. The ''handedness'' in both chirality and helicity relate to the rotation of a particle while it proceeds in linear motion with reference to the human hands. The thumb of the hand points towards the direction of linear motion whilst the fingers curl into the palm, representing the direction of rotation of the particle (i.e. clockwise and counterclockwise). Depending on the linear and rotational motion, the particle can either be defined by left-handedness or right-handedness. A symmetry transformation between the two is called
parity Parity may refer to: * Parity (computing) ** Parity bit in computing, sets the parity of data for the purpose of error detection ** Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the ...
. Invariance under parity by a
Dirac fermion In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. The vast majority of fermions – perhaps all – fall under this category. Description In particle physics, all fermions in the standard mo ...
is called ''chiral symmetry''.


Electromagnetism

Electromagnetic waves can have handedness associated with their polarization. Polarization of an
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
is the property that describes the orientation, i.e., the time-varying direction and
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
, of the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
vector. For example, the electric field vectors of left-handed or right-handed circularly polarized waves form helices of opposite handedness in space. Circularly polarized waves of opposite handedness propagate through chiral media at different speeds ( circular birefringence) and with different losses ( circular dichroism). Both phenomena are jointly known as optical activity. Circular birefringence causes rotation of the polarization state of electromagnetic waves in chiral media and can cause a negative index of refraction for waves of one handedness when the effect is sufficiently large. While optical activity occurs in structures that are chiral in three dimensions (such as helices), the concept of chirality can also be applied in two dimensions. 2D-chiral patterns, such as flat spirals, cannot be superimposed with their mirror image by translation or rotation in two-dimensional space (a plane). 2D chirality is associated with directionally asymmetric transmission (reflection and absorption) of circularly polarized waves. 2D-chiral materials, which are also anisotropic and lossy exhibit different total transmission (reflection and absorption) levels for the same circularly polarized wave incident on their front and back. The asymmetric transmission phenomenon arises from different, e.g. left-to-right, circular polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as circular conversion dichroism. Like the twist of a 2d-chiral pattern appears reversed for opposite directions of observation, 2d-chiral materials have interchanged properties for left-handed and right-handed circularly polarized waves that are incident on their front and back. In particular left-handed and right-handed circularly polarized waves experience opposite directional transmission (reflection and absorption) asymmetries. While optical activity is associated with 3d chirality and circular conversion is associated with 2d chirality, both effects have also been observed in structures that are not chiral by themselves. For the observation of these chiral electromagnetic effects, chirality does not have to be an intrinsic property of the material that interacts with the electromagnetic wave. Instead, both effects can also occur when the propagation direction of the electromagnetic wave together with the structure of an (achiral) material form a chiral experimental arrangement. This case, where the mutual arrangement of achiral components forms a chiral (experimental) arrangement, is known as extrinsic chirality. Chiral mirrors are a class of metamaterials that reflect circularly polarized light of a certain helicity in a handedness-preserving manner, while absorbing circular polarization of the opposite handedness. However, most absorbing chiral mirrors operate only in a narrow frequency band, as limited by the causality principle. Employing a different design methodology that allows undesired waves to pass through instead of absorbing the undesired waveform, chiral mirrors are able to show good broadband performance.


Chemistry

A ''chiral molecule'' is a type of
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
that has a non-superposable
mirror image A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical effect it results from reflection off from substance ...
. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom. The term "chiral" in general is used to describe the object that is non-superposable on its mirror image. In chemistry, chirality usually refers to molecules. Two mirror images of a chiral molecule are called
enantiomer In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical anti ...
s or optical isomers. Pairs of enantiomers are often designated as " right-", "left-handed" or, if they have no bias, "achiral". As polarized light passes through a chiral molecule, the plane of polarization, when viewed along the axis toward the source, will be rotated clockwise (to the right) or anticlockwise (to the left). A right handed rotation is dextrorotary (d); that to the left is levorotary (l). The d- and l-isomers are the same compound but are called enantiomers. An equimolar mixture of the two optical isomers, which is called a
racemic mixture In chemistry, a racemic mixture, or racemate (), is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule or salt. Racemic mixtures are rare in nature, but many compounds are produced industrially as racemates. ...
, will produce no net rotation of polarized light as it passes through. Left handed molecules have l- prefixed to their names; d- is prefixed to right handed molecules. However, this ''d-'' and ''l-'' notation of distinguishing enantiomers does not say anything about the actual spatial arrangement of the ligands/substituents around the stereogenic center, which is defined as configuration. Another nomenclature system employed to specify configuration is Fischer convention. This is also referred to as the D- and L-system. Here the relative configuration is assigned with reference to D-(+)-Glyceraldehyde and L-(-)-Glyceraldehyde, being taken as standard. Fischer convention is widely used in sugar chemistry and for α-amino acids. Due to the drawbacks of Fischer convention, it is almost entirely replaced by Cahn-Ingold-Prelog convention, also known as the sequence rule or R and S nomenclature. This was further extended to assign absolute configuration to ''cis-trans'' isomers with the E-Z notation. Molecular chirality is of interest because of its application to stereochemistry in inorganic chemistry,
organic chemistry Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J ...
,
physical chemistry Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistica ...
,
biochemistry Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, and supramolecular chemistry. More recent developments in chiral chemistry include the development of chiral inorganic nanoparticles that may have the similar tetrahedral geometry as chiral centers associated with sp3 carbon atoms traditionally associated with chiral compounds, but at larger scale. Helical and other symmetries of chiral nanomaterials were also obtained.


Biology

All of the known life-forms show specific chiral properties in chemical structures as well as macroscopic anatomy, development and behavior. In any specific organism or evolutionarily related set thereof, individual compounds, organs, or behavior are found in the same single enantiomorphic form. Deviation (having the opposite form) could be found in a small number of chemical compounds, or certain organ or behavior but that variation strictly depends upon the genetic make up of the organism. From chemical level (molecular scale), biological systems show extreme stereospecificity in synthesis, uptake, sensing, metabolic processing. A living system usually deals with two enantiomers of the same compound in drastically different ways. In biology, homochirality is a common property of amino acids and
carbohydrates In organic chemistry, a carbohydrate () is a biomolecule consisting of carbon (C), hydrogen (H) and oxygen (O) atoms, usually with a hydrogen–oxygen atom ratio of 2:1 (as in water) and thus with the empirical formula (where ''m'' may or m ...
. The chiral protein-making amino acids, which are translated through the ribosome from genetic coding, occur in the L form. However, D-amino acids are also found in nature. The monosaccharides (carbohydrate-units) are commonly found in D-configuration. DNA double helix is chiral (as any kind of helix is chiral), and B-form of DNA shows a right-handed turn. Sometimes, when two enantiomers of a compound found in organisms, they significantly differ in their taste, smell and other biological actions. For example, (+)-limonene found in orange (causing its smell), and (–)-limonene found in lemons (causing its smell), show different smells due to different biochemical interactions at human nose. (+)- Carvone is responsible for the smell of caraway seed oil, whereas (–)-carvone is responsible for smell of spearmint oil. Also, for artificial compounds, including medicines, in case of chiral drugs, the two enantiomers sometimes show remarkable difference in effect of their biological actions. Darvon ( dextropropoxyphene) is a painkiller, whereas its enantiomer, Novrad (
levopropoxyphene Levopropoxyphene is an antitussive. It is an optical isomer of dextropropoxyphene. The racemic mixture is called propoxyphene. Only the dextro-isomer (dextropropoxyphene) has an analgesic effect; the levo-isomer appears to exert only an antitussi ...
) is an anti-cough agent. In case of penicillamine, the (''S''-isomer is used in the treatment of primary chronic arthritis, whereas the (''R'')-isomer has no therapeutic effect, as well as being highly toxic. In some cases, the less therapeutically active enantiomer can cause side effects. For example, (''S''-naproxen is an analgesic but the (''R''-isomer causes renal problems. In such situations where one of the enantiomers of a racemic drug is active and the other partner has undesirable or toxic effect one may switch from racemate to a single enantiomer drug for a better therapeutic valu

Such a switching from a racemic drug to an enantiopure drug is called a chiral switch. The naturally occurring plant form of alpha-tocopherol (
vitamin E Vitamin E is a group of eight fat soluble compounds that include four tocopherols and four tocotrienols. Vitamin E deficiency, which is rare and usually due to an underlying problem with digesting dietary fat rather than from a diet low in vi ...
) is RRR-α-tocopherol whereas the synthetic form (all-racemic vitamin E, or dl-tocopherol) is equal parts of the stereoisomers RRR, RRS, RSS, SSS, RSR, SRS, SRR, and SSR with progressively decreasing biological equivalency, so that 1.36 mg of dl-tocopherol is considered equivalent to 1.0 mg of d-tocopherol. Macroscopic examples of chirality are found in the plant kingdom, the animal kingdom and all other groups of organism. A simple example is the coiling direction of any climber plant, which can grow to form either a left- or right-handed helix. In anatomy, chirality is found in the imperfect mirror image symmetry of many kinds of animal bodies. Organisms such as
gastropod The gastropods (), commonly known as snails and slugs, belong to a large taxonomic class of invertebrates within the phylum Mollusca called Gastropoda (). This class comprises snails and slugs from saltwater, from freshwater, and from land. T ...
s exhibit chirality in their coiled shells, resulting in an asymmetrical appearance. Over 90% of gastropod species have ''dextral'' (right-handed) shells in their coiling, but a small minority of species and genera are virtually always ''sinistral'' (left-handed). A very few species (for example ''
Amphidromus perversus ''Amphidromus perversus'' is a species of air-breathing land snail, a terrestrial pulmonate gastropod mollusk in the family Camaenidae. MolluscaBase eds. (2020). MolluscaBase. Amphidromus perversus (Linnaeus, 1758). Accessed through: World R ...
'') show an equal mixture of dextral and sinistral individuals. In humans, chirality (also referred to as ''handedness'' or ''laterality'') is an attribute of humans defined by their unequal distribution of fine motor skill between the left and right
hands A hand is a prehensile, multi- fingered appendage located at the end of the forearm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs. A few other vertebrates such as the koala (which has two opposable thumbs on eac ...
. An individual who is more
dexterous Fine motor skill (or dexterity) is the coordination of small muscles in movement with the eyes, hands and fingers. The complex levels of manual dexterity that humans exhibit can be related to the nervous system. Fine motor skills aid in the gro ...
with the right hand is called '' right-handed'', and one who is more skilled with the left is said to be '' left-handed''. Chirality is also seen in the study of
facial asymmetry Facial symmetry is one specific measure of bodily symmetry. Along with traits such as averageness and youthfulness it influences judgments of aesthetic traits of physical attractiveness and beauty. For instance, in mate selection, people have b ...
. In the case of the health condition '' situs inversus totalis'', in which all the internal organs are flipped horizontally (i.e. the heart placed slightly to the right instead of the left), chirality poses some problems should the patient require a liver or heart transplant, as these organs are chiral, thus meaning that the blood vessels which supply these organs would need to be rearranged should a normal, non ''situs inversus'' (''
situs solitus Situs solitus is the medical term referring to the normal position of thoracic and abdominal organs. Anatomically, this means that the heart is on the left with the pulmonary atrium on the right and the systemic atrium on the left along with the ...
'') organ be required. In the monocot bloodroot family, the species of the genera ''
Wachendorfia ''Wachendorfia'' is a genus of perennial herbaceous plants that is assigned to the bloodroot family. The plants have a perennial rootstock with red sap. From the rootstock emerge lance- or line-shaped, sometime sickle-shaped, pleated, simple ...
'' and ''
Barberetta ''Barberetta'' is a genus of herbaceous perennial plants in the family Haemodoraceae. It contains only one known species, ''Barberetta aurea''. Description ''Barberetta aurea'' grows to up to high from a tuberous rootstock and develops abou ...
'' have only individuals that either have the style points to the right or the style pointed to the left, with both morphs appearing within the same populations. This is thought to increase
outcrossing Out-crossing or out-breeding is the technique of crossing between different breeds. This is the practice of introducing distantly related genetic material into a breeding line, thereby increasing genetic diversity. Outcrossing can be a usefu ...
and so boost genetic diversity, which in turn may help to survive in a changing environment. Remarkably, the related genus ''
Dilatris ''Dilatris'' is a genus of four species of evergreen perennial herbaceous plants of up to high, that are assigned to the bloodroot family. The plants have hairless, line- to lance-shaped leaves set in a fan that emerges from a red or orange co ...
'' also has chiraly dimorphic flowers, but here both morphs occur on the same plant. In flatfish, the summer flounder or fluke are left-eyed, while halibut are right-eyed.


See also

* Handedness * Chiral drugs * Chiral switch *
Chiral inversion Chiral inversion is the process of conversion of one enantiomer of a chiral molecule to its mirror-image version with no other change in the molecule. Chiral inversion happens depending on various factors (viz. biological-, solvent-, light-, temper ...
* Metachirality * Orientation (space) * Sinistral and dextral *
Tendril perversion Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed. Such a reversal of chirality is commonly seen in helical plant tendril ...
* Chirality (physics)


References


External links

* {{Navbox stereochemistry 1890s neologisms Biochemistry Origin of life Stereochemistry Pharmacology de:Chiralität (Chemie)