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In
molecular biology Molecular biology is the branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, P ...
, the term double helix refers to the structure formed by
double-stranded A base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobase 230px, Pyrimidine nucleobases are simple ring molecules. Nucleobases, also known as ''nitrogenous bases'' or often simply ''bases'', are nitr ...
molecules of
nucleic acid Nucleic acids are biopolymer Biopolymers are natural polymer A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules, or macromolecule ...

nucleic acid
s such as
DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral gro ...

DNA
. The double
helical Helical may refer to: *Helix, the mathematical concept for the shape * Helical spring, a coilspring *Helical plc, a British property company, once a maker of steel bar stock * Helicoil, a mechanical thread repairing insert * H-el-ical//, stage name ...

helical
structure of a nucleic acid complex arises as a consequence of its
secondary structure Biomolecular structure is the intricate folded, three-dimensional shape that is formed by a molecule A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an elect ...
, and is a fundamental component in determining its
tertiary structure Biomolecular structure is the intricate folded, three-dimensional shape that is formed by a molecule A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an elect ...
. The term entered popular culture with the publication in 1968 of ''
The Double Helix ''The Double Helix: A Personal Account of the Discovery of the Structure of DNA'' is an autobiographical account of the discovery of the double helix In molecular biology, the term double helix refers to the structure formed by double-strand ...

The Double Helix
: A Personal Account of the Discovery of the Structure of DNA'' by
James Watson James Dewey Watson (born April 6, 1928) is an American molecular biologist, geneticist A geneticist is a biologist Francesco Redi, the founder of biology, is recognized to be one of the greatest biologists of all time A biologist is a ...

James Watson
. The DNA double helix
biopolymer Biopolymers are natural polymer A polymer (; Greek ''poly- Poly, from the Greek :wikt:πολύς, πολύς meaning "many" or "much", may refer to: Businesses * China Poly Group Corporation, a Chinese business group, and its subsidiaries ...
of
nucleic acid Nucleic acids are biopolymer Biopolymers are natural polymer A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules, or macromolecule ...

nucleic acid
is held together by
nucleotide Nucleotides are organic molecules , CH4; is among the simplest organic compounds. In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen chemical bond, bonds. Due to carbon's ability to Catenation, ...

nucleotide
s which
base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids Nucleic acids are biopolymer Biopolymers are natural polymers produced by the cells of Organism, living organisms. Biopolymers consist of monomeric units that are Covalent_ ...
together. In
B-DNA In molecular biology Molecular biology is the branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, ...
, the most common double helical structure found in nature, the double helix is right-handed with about 10–10.5 base pairs per turn. The double helix structure of DNA contains a ''major groove'' and ''minor groove''. In B-DNA the major groove is wider than the minor groove. Given the difference in widths of the major groove and minor groove, many proteins which bind to B-DNA do so through the wider major groove.


History

The double-helix model of
DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral gro ...

DNA
structure was first published in the journal ''
Nature Nature, in the broadest sense, is the natural, physical, material world or universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter an ...
'' by
James Watson James Dewey Watson (born April 6, 1928) is an American molecular biologist, geneticist A geneticist is a biologist Francesco Redi, the founder of biology, is recognized to be one of the greatest biologists of all time A biologist is a ...

James Watson
and
Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British molecular biologist, biophysicist, and neuroscientist A neuroscientist (or neurobiologist) is a scientist A scientist is a person who conducts Scientific method, scie ...

Francis Crick
in 1953, (X,Y,Z coordinates in 1954) based on the work of
Rosalind Franklin Rosalind Elsie Franklin (25 July 192016 April 1958) was an English chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin Medieval Latin was the form of Latin Latin (, or , ) is a classica ...

Rosalind Franklin
and her student
Raymond Gosling Raymond George Gosling (15 July 1926 – 18 May 2015) was a British scientist. While a PhD student at King's College, London he worked under the supervision of Maurice Wilkins and Rosalind Franklin. The crystallographic experiments of Franklin ...

Raymond Gosling
, who took the crucial X-ray diffraction image of DNA labeled as "
Photo 51 ' ''Photo 51'' is an X-ray diffraction X-ray crystallography (XRC) is the experimental science determining the atomic and molecular structure of a crystal A crystal or crystalline solid is a solid material whose constituents (such as ...
", and
Maurice Wilkins Maurice Hugh Frederick Wilkins (15 December 1916 – 5 October 2004) was a New Zealand-born and whose research spanned multiple areas of physics and biophysics, contributing to the scientific understanding of , , and , and to the developme ...
, Alexander Stokes, and
Herbert Wilson Herbert Rees Wilson Fellow of the Royal Society of Edinburgh, FRSE (20 March 1929 – 22 May 2008) was a physicist, who was one of the team who worked on the structure of DNA at King's College London, under the direction of John Randall (physicist ...
, and base-pairing chemical and biochemical information by
Erwin Chargaff Erwin Chargaff (11 August 1905 – 20 June 2002) was an Austro-Hungarian-born American biochemist Biochemists are scientists who are trained in biochemistry Biochemistry or biological chemistry, is the study of chemical process In a scie ...
. The prior model was
triple-stranded DNA Triple-stranded DNA (also known as H-DNA or Triplex-DNA) is a DNA structure in which three oligonucleotides wind around each other and form a triple helix. In triple-stranded DNA, the third strand binds to a Nucleic acid double helix#Helix geometr ...
. The realization that the structure of DNA is that of a double-helix elucidated the mechanism of
base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids Nucleic acids are biopolymer Biopolymers are natural polymers produced by the cells of Organism, living organisms. Biopolymers consist of monomeric units that are Covalent_ ...
ing by which genetic information is stored and copied in living organisms and is widely considered one of the most important scientific discoveries of the 20th century. Crick, Wilkins, and Watson each received one third of the 1962
Nobel Prize in Physiology or Medicine The Nobel Prize in Physiology or Medicine is awarded yearly by the Nobel Assembly , native_name_lang = , image = Nobel Assembly at Karolinska Institutet.jpeg , size = , motto = , formation = 190113 March 1978(as a forma ...
for their contributions to the discovery.


Nucleic acid hybridization

Hybridization is the process of
complementary A complement is often something that completes something else, or at least adds to it in some useful way. Thus it may be: * Complement (linguistics), a word or phrase having a particular syntactic role ** Subject complement, a word or phrase addi ...
base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids Nucleic acids are biopolymer Biopolymers are natural polymers produced by the cells of Organism, living organisms. Biopolymers consist of monomeric units that are Covalent_ ...
s binding to form a double helix. Melting is the process by which the interactions between the strands of the double helix are broken, separating the two nucleic acid strands. These bonds are weak, easily separated by gentle heating,
enzyme Enzymes () are proteins that act as biological catalysts (biocatalysts). Catalysts accelerate chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates in ...

enzyme
s, or mechanical force. Melting occurs preferentially at certain points in the nucleic acid. ''T'' and ''A'' rich regions are more easily melted than ''C'' and ''G'' rich regions. Some base steps (pairs) are also susceptible to DNA melting, such as ''T A'' and ''T G''. These mechanical features are reflected by the use of sequences such as '' TATA'' at the start of many genes to assist RNA polymerase in melting the DNA for transcription. Strand separation by gentle heating, as used in
polymerase chain reaction Polymerase chain reaction (PCR) is a method widely used to rapidly make millions to billions of copies (complete copies or partial copies) of a specific DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM. ...

polymerase chain reaction
(PCR), is simple, providing the molecules have fewer than about 10,000 base pairs (10 kilobase pairs, or 10 kbp). The intertwining of the DNA strands makes long segments difficult to separate. The cell avoids this problem by allowing its DNA-melting enzymes (
helicase Helicases are a class of enzyme Enzymes () are protein Proteins are large s and s that comprise one or more long chains of . Proteins perform a vast array of functions within organisms, including , , , providing and , and from one ...

helicase
s) to work concurrently with
topoisomerase Topoisomerases (or DNA topoisomerases) are enzymes that participate in the overwinding or underwinding of DNA. The winding problem of DNA arises due to the intertwined nature of its double-helical structure. During DNA replication and transcriptio ...
s, which can chemically cleave the phosphate backbone of one of the strands so that it can swivel around the other.
Helicase Helicases are a class of enzyme Enzymes () are protein Proteins are large s and s that comprise one or more long chains of . Proteins perform a vast array of functions within organisms, including , , , providing and , and from one ...

Helicase
s unwind the strands to facilitate the advance of sequence-reading enzymes such as
DNA polymerase A DNA polymerase is a member of a family of enzyme Enzymes () are s that act as s (biocatalysts). Catalysts accelerate . The molecules upon which enzymes may act are called , and the enzyme converts the substrates into different molecules ...

DNA polymerase
.


Base pair geometry

The geometry of a base, or base pair step can be characterized by 6 coordinates: shift, slide, rise, tilt, roll, and twist. These values precisely define the location and orientation in space of every base or base pair in a nucleic acid molecule relative to its predecessor along the axis of the helix. Together, they characterize the helical structure of the molecule. In regions of DNA or RNA where the ''normal'' structure is disrupted, the change in these values can be used to describe such disruption. For each base pair, considered relative to its predecessor, there are the following base pair geometries to consider: *Shear *Stretch *Stagger *Buckle *Propeller: rotation of one base with respect to the other in the same base pair. *Opening *Shift: displacement along an axis in the base-pair plane perpendicular to the first, directed from the minor to the major groove. *Slide: displacement along an axis in the plane of the base pair directed from one strand to the other. *Rise: displacement along the helix axis. *Tilt: rotation around the shift axis. *Roll: rotation around the slide axis. *Twist: rotation around the rise axis. *x-displacement *y-displacement *inclination *tip *pitch: the height per complete turn of the helix. Rise and twist determine the handedness and pitch of the helix. The other coordinates, by contrast, can be zero. Slide and shift are typically small in B-DNA, but are substantial in A- and Z-DNA. Roll and tilt make successive base pairs less parallel, and are typically small. Note that "tilt" has often been used differently in the scientific literature, referring to the deviation of the first, inter-strand base-pair axis from perpendicularity to the helix axis. This corresponds to slide between a succession of base pairs, and in helix-based coordinates is properly termed "inclination".


Helix geometries

At least three DNA conformations are believed to be found in nature,
A-DNA A-DNA is one of the possible double helical structures which DNA can adopt. A-DNA is thought to be one of three biologically active double helical structures along with B-DNA and Z-DNA. It is a right-handed double helix fairly similar to the mor ...
, B-DNA, and
Z-DNA Z-DNA is one of the many possible double helical structures of DNA. It is a left-handed double helical structure in which the helix winds to the left in a zigzag pattern, instead of to the right, like the more common B-DNA In molecular biolog ...
. The ''B'' form described by
James Watson James Dewey Watson (born April 6, 1928) is an American molecular biologist, geneticist A geneticist is a biologist Francesco Redi, the founder of biology, is recognized to be one of the greatest biologists of all time A biologist is a ...

James Watson
and
Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British molecular biologist, biophysicist, and neuroscientist A neuroscientist (or neurobiologist) is a scientist A scientist is a person who conducts Scientific method, scie ...

Francis Crick
is believed to predominate in cells. It is 23.7 wide and extends 34 Å per 10 bp of sequence. The double helix makes one complete turn about its axis every 10.4–10.5 base pairs in solution. This frequency of twist (termed the helical ''pitch'') depends largely on stacking forces that each base exerts on its neighbours in the chain. The
absolute configuration An absolute configuration refers to the spatial arrangement of the atoms of a chirality (chemistry), chiral molecular entity (or group) and its stereochemical description e.g. R or S, referring to Rectus, or Sinister, respectively. Absolute confi ...
of the bases determines the direction of the helical curve for a given conformation. A-DNA and Z-DNA differ significantly in their geometry and dimensions to B-DNA, although still form helical structures. It was long thought that the A form only occurs in dehydrated samples of DNA in the laboratory, such as those used in
crystallographic Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure). The word "crystallography" is derived from the Greek words ''crystallon'' "cold drop, frozen drop", with its mean ...

crystallographic
experiments, and in hybrid pairings of DNA and
RNA Ribonucleic acid (RNA) is a polymer A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules, or macromolecules, composed of many Re ...

RNA
strands, but DNA dehydration does occur
in vivo Studies Study or studies may refer to: General * Education **Higher education * Clinical trial * Experiment * Observational study * Research * Study skills, abilities and approaches applied to learning Other * Study (art), a drawing or series ...
, and A-DNA is now known to have biological functions. Segments of DNA that cells have
methylated In the chemical sciences, methylation denotes the addition of a methyl group on a substrate, or the substitution of an atom (or group) by a methyl group. Methylation is a form of alkylation, with a methyl group replacing a hydrogen atom. These t ...

methylated
for regulatory purposes may adopt the Z geometry, in which the strands turn about the helical axis the opposite way to A-DNA and B-DNA. There is also evidence of protein-DNA complexes forming Z-DNA structures. Other conformations are possible; A-DNA, B-DNA,
C-DNA C-DNA, also known as C-form DNA, is one of many possible double helical conformations of DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, ...
, E-DNA, L-DNA (the
enantiomer In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they und ...

enantiomer
ic form of D-DNA), P-DNA, S-DNA, Z-DNA, etc. have been described so far. In fact, only the letters F, Q, U, V, and Y are available to describe any new DNA structure that may appear in the future. However, most of these forms have been created synthetically and have not been observed in naturally occurring biological systems. There are also
triple-stranded DNA Triple-stranded DNA (also known as H-DNA or Triplex-DNA) is a DNA structure in which three oligonucleotides wind around each other and form a triple helix. In triple-stranded DNA, the third strand binds to a Nucleic acid double helix#Helix geometr ...
forms and quadruplex forms such as the
G-quadruplex In molecular biology, G-quadruplex secondary structures (G4) are formed in nucleic acids by sequences that are rich in guanine Guanine () (symbol A symbol is a mark, sign, or word In linguistics, a word of a spoken language can be defin ...

G-quadruplex
and the
i-motif i-motif DNA, short for intercalated-motif DNA, are cytosine-rich four-stranded quadruplex DNA structures, similar to the G-quadruplex structures that are formed in guanine-rich regions of DNA. History This structure was first discovered in 1993 ...
.


Grooves

Twin helical strands form the DNA backbone. Another double helix may be found by tracing the spaces, or grooves, between the strands. These voids are adjacent to the base pairs and may provide a
binding site Binding may refer to: Computing * Binding, associating a network socket Network and networking may refer to: Arts, entertainment, and media * Network (1976 film), ''Network'' (1976 film), a 1976 American film * Network (2019 film), ''Network'' ...
. As the strands are not directly opposite each other, the grooves are unequally sized. One groove, the major groove, is 22 Å wide and the other, the minor groove, is 12 Å wide. The narrowness of the minor groove means that the edges of the bases are more accessible in the major groove. As a result, proteins like
transcription factor In molecular biology Molecular biology is the branch of biology that seeks to understand the molecule, molecular basis of biological activity in and between Cell (biology), cells, including biomolecule, molecular synthesis, modification, m ...
s that can bind to specific sequences in double-stranded DNA usually make contacts to the sides of the bases exposed in the major groove. This situation varies in unusual conformations of DNA within the cell ''(see below)'', but the major and minor grooves are always named to reflect the differences in size that would be seen if the DNA is twisted back into the ordinary B form.


Non-double helical forms

Alternative non-helical models were briefly considered in the late 1970s as a potential solution to problems in
DNA replication In , DNA replication is the of producing two identical replicas of DNA from one original molecule. DNA replication occurs in all acting as the most essential part for . This is essential for cell division during growth and repair of damaged tis ...

DNA replication
in
plasmid A plasmid is a small, extrachromosomal DNA Extrachromosomal DNA (abbreviated ecDNA) is any DNA that is found off the chromosome A chromosome is a long DNA molecule with part or all of the genetic material of an organism. Most eukaryo ...
s and
chromatin Chromatin is a complex of DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecu ...
. However, the models were set aside in favor of the double-helical model due to subsequent experimental advances such as
X-ray crystallography X-ray crystallography (XRC) is the experimental science determining the atomic and molecular structure of a crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a ...

X-ray crystallography
of DNA duplexes and later the nucleosome core particle, and the discovery of
topoisomerase Topoisomerases (or DNA topoisomerases) are enzymes that participate in the overwinding or underwinding of DNA. The winding problem of DNA arises due to the intertwined nature of its double-helical structure. During DNA replication and transcriptio ...
s. Also, the non-double-helical models are not currently accepted by the mainstream scientific community.


Bending

DNA is a relatively rigid polymer, typically modelled as a
worm-like chainThe worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecule File:Pentacene on Ni(1 ...
. It has three significant degrees of freedom; bending, twisting, and compression, each of which cause certain limits on what is possible with DNA within a cell. Twisting-torsional stiffness is important for the circularisation of DNA and the orientation of DNA bound proteins relative to each other and bending-axial stiffness is important for DNA wrapping and circularisation and protein interactions. Compression-extension is relatively unimportant in the absence of high tension.


Persistence length, axial stiffness

DNA in solution does not take a rigid structure but is continually changing conformation due to thermal vibration and collisions with water molecules, which makes classical measures of rigidity impossible to apply. Hence, the bending stiffness of DNA is measured by the persistence length, defined as: This value may be directly measured using an
atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy Scanning probe microscopy (SPM) is a branch of microscopy that forms images of surfaces using a physical probe that scans ...
to directly image DNA molecules of various lengths. In an aqueous solution, the average persistence length is 46–50 nm or 140–150 base pairs (the diameter of DNA is 2 nm), although can vary significantly. This makes DNA a moderately stiff molecule. The persistence length of a section of DNA is somewhat dependent on its sequence, and this can cause significant variation. The variation is largely due to base stacking energies and the residues which extend into the
minor Minor may refer to: * Minor (law), a person under the age of certain legal activities. ** A person who has not reached the age of majority * Academic minor, a secondary field of study in undergraduate education Music theory *Minor chord ** Barbe ...
and
major groove In molecular biology, the term double helix refers to the structure formed by double-stranded molecules of nucleic acids such as DNA. The double helical structure of a nucleic acid complex arises as a consequence of its secondary structure ...
s.


Models for DNA bending

At length-scales larger than the persistence length, the entropic flexibility of DNA is remarkably consistent with standard
polymer physicsPolymer physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entiti ...
models, such as the ''Kratky-Porod''
worm-like chainThe worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecule File:Pentacene on Ni(1 ...
model. Consistent with the
worm-like chainThe worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecule File:Pentacene on Ni(1 ...
model is the observation that bending DNA is also described by
Hooke's law The balance wheel at the core of many mechanical clocks and watches depends on Hooke's law. Since the torque generated by the coiled spring is proportional to the angle turned by the wheel, its oscillations have a nearly constant period. Hooke ...
at very small (sub-
piconewton The newton (symbol: N) is the International System of Units (SI) SI derived unit, derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's laws of motion#Newton's second law, ...
) forces. For DNA segments less than the persistence length, the bending force is approximately constant and behaviour deviates from the worm-like chain predictions. This effect results in unusual ease in circularising small DNA molecules and a higher probability of finding highly bent sections of DNA.


Bending preference

DNA molecules often have a preferred direction to bend, i.e.,
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions as opposed to isotropy Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, ...
bending. This is, again, due to the properties of the bases which make up the DNA sequence - a random sequence will have no preferred bend direction, i.e., isotropic bending. Preferred DNA bend direction is determined by the stability of stacking each base on top of the next. If unstable base stacking steps are always found on one side of the DNA helix then the DNA will preferentially bend away from that direction. As bend angle increases then steric hindrances and ability to roll the residues relative to each other also play a role, especially in the minor groove. ''A'' and ''T'' residues will be preferentially be found in the minor grooves on the inside of bends. This effect is particularly seen in DNA-protein binding where tight DNA bending is induced, such as in
nucleosome A nucleosome is the basic structural unit of DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon ...

nucleosome
particles. See base step distortions above. DNA molecules with exceptional bending preference can become intrinsically bent. This was first observed in
trypanosoma ''Trypanosoma'' is a genus Genus /ˈdʒiː.nəs/ (plural genera /ˈdʒen.ər.ə/) is a taxonomic rank In biological classification In biology Biology is the natural science that studies life and living organisms, including th ...

trypanosoma
tid
kinetoplast A kinetoplast is a network of circular DNA (called kDNA) inside a large mitochondrion that contains many copies of the mitochondrial genome. The most common kinetoplast structure is a disk, but they have been observed in other arrangements. Kinetopl ...
DNA. Typical sequences which cause this contain stretches of 4-6 ''T'' and ''A'' residues separated by ''G'' and ''C'' rich sections which keep the A and T residues in phase with the minor groove on one side of the molecule. For example: The intrinsically bent structure is induced by the 'propeller twist' of base pairs relative to each other allowing unusual bifurcated Hydrogen-bonds between base steps. At higher temperatures this structure is denatured, and so the intrinsic bend is lost. All DNA which bends anisotropically has, on average, a longer persistence length and greater axial stiffness. This increased rigidity is required to prevent random bending which would make the molecule act isotropically.


Circularization

DNA circularization depends on both the axial (bending) stiffness and torsional (rotational) stiffness of the molecule. For a DNA molecule to successfully circularize it must be long enough to easily bend into the full circle and must have the correct number of bases so the ends are in the correct rotation to allow bonding to occur. The optimum length for circularization of DNA is around 400 base pairs (136 nm), with an integral number of turns of the DNA helix, i.e., multiples of 10.4 base pairs. Having a non integral number of turns presents a significant energy barrier for circularization, for example a 10.4 x 30 = 312 base pair molecule will circularize hundreds of times faster than 10.4 x 30.5 ≈ 317 base pair molecule. The bending of short circularized DNA segments is non-uniform. Rather, for circularized DNA segments less than the persistence length, DNA bending is localised to 1-2 kinks that form preferentially in AT-rich segments. If a nick is present, bending will be localised to the nick site.


Stretching


Elastic stretching regime

Longer stretches of DNA are entropically elastic under tension. When DNA is in solution, it undergoes continuous structural variations due to the energy available in the
thermal bath A spa is a location where mineral-rich spring (hydrology), spring water (and sometimes seawater) is used to give medicinal baths. Spa towns or spa resorts (including hot springs resorts) typically offer various health treatments, which are also ...
of the solvent. This is due to the thermal vibration of the molecule combined with continual collisions with water molecules. For reasons, more compact relaxed states are thermally accessible than stretched out states, and so DNA molecules are almost universally found in a tangled relaxed layouts. For this reason, one molecule of DNA will stretch under a force, straightening it out. Using
optical tweezers Optical tweezers (originally called single-beam gradient force trap) are scientific instruments that use a highly focused laser A laser is a device that emits light Light or visible light is electromagnetic radiation within the port ...
, the entropic stretching behavior of DNA has been studied and analyzed from a
polymer physicsPolymer physics is the field of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entiti ...
perspective, and it has been found that DNA behaves largely like the ''Kratky-Porod''
worm-like chainThe worm-like chain (WLC) model in polymer physics is used to describe the behavior of polymers A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecule File:Pentacene on Ni(1 ...
model under physiologically accessible energy scales.


Phase transitions under stretching

Under sufficient tension and positive torque, DNA is thought to undergo a
phase transition In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in ...
with the bases splaying outwards and the phosphates moving to the middle. This proposed structure for overstretched DNA has been called ''P-form DNA'', in honor of
Linus Pauling Linus Carl Pauling (; February 28, 1901 – August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific t ...

Linus Pauling
who originally presented it as a possible structure of DNA. Evidence from mechanical stretching of DNA in the absence of imposed torque points to a transition or transitions leading to further structures which are generally referred to as ''S-form DNA''. These structures have not yet been definitively characterised due to the difficulty of carrying out atomic-resolution imaging in solution while under applied force although many computer simulation studies have been made (for example,). Proposed S-DNA structures include those which preserve base-pair stacking and hydrogen bonding (GC-rich), while releasing extension by tilting, as well as structures in which partial melting of the base-stack takes place, while base-base association is nonetheless overall preserved (AT-rich). Periodic fracture of the base-pair stack with a break occurring once per three bp (therefore one out of every three bp-bp steps) has been proposed as a regular structure which preserves planarity of the base-stacking and releases the appropriate amount of extension, with the term "Σ-DNA" introduced as a mnemonic, with the three right-facing points of the Sigma character serving as a reminder of the three grouped base pairs. The Σ form has been shown to have a sequence preference for GNC motifs which are believed under the
GNC hypothesis The GNC hypothesis or GNC-SNS primeval genetic code hypothesis refers to a hypothesis about the origin of genes. It suggests the universal genetic code originated not from a three-amino acid system, but from a four-amino acid system. It is this G ...
to be of evolutionary importance.


Supercoiling and topology

The B form of the DNA helix twists 360° per 10.4-10.5 bp in the absence of torsional strain. But many molecular biological processes can induce torsional strain. A DNA segment with excess or insufficient helical twisting is referred to, respectively, as positively or negatively ''
supercoil DNA supercoiling refers to the amount of twist in a particular DNA strand, which determines the amount of strain on it. A given strand may be “positively supercoiled” or “negatively supercoiled” (more or less tightly wound). The amount o ...
ed''. DNA ''in vivo'' is typically negatively supercoiled, which facilitates the unwinding (melting) of the double-helix required for RNA transcription. Within the cell most DNA is topologically restricted. DNA is typically found in closed loops (such as
plasmid A plasmid is a small, extrachromosomal DNA Extrachromosomal DNA (abbreviated ecDNA) is any DNA that is found off the chromosome A chromosome is a long DNA molecule with part or all of the genetic material of an organism. Most eukaryo ...
s in prokaryotes) which are topologically closed, or as very long molecules whose diffusion coefficients produce effectively topologically closed domains. Linear sections of DNA are also commonly bound to proteins or physical structures (such as membranes) to form closed topological loops.
Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British molecular biologist, biophysicist, and neuroscientist A neuroscientist (or neurobiologist) is a scientist A scientist is a person who conducts Scientific method, scie ...

Francis Crick
was one of the first to propose the importance of linking numbers when considering DNA supercoils. In a paper published in 1976, Crick outlined the problem as follows:
In considering supercoils formed by closed double-stranded molecules of DNA certain mathematical concepts, such as the linking number and the twist, are needed. The meaning of these for a closed ribbon is explained and also that of the writhing number of a closed curve. Some simple examples are given, some of which may be relevant to the structure of chromatin.
Analysis of DNA topology uses three values: *''L'' = linking number - the number of times one DNA strand wraps around the other. It is an integer for a closed loop and constant for a closed topological domain. *''T'' = twist - total number of turns in the double stranded DNA helix. This will normally tend to approach the number of turns that a topologically open double stranded DNA helix makes free in solution: number of bases/10.5, assuming there are no intercalating agents (e.g.,
ethidium bromide Ethidium bromide (or homidium bromide, chloride salt homidium chloride) is an intercalating agent commonly used as a fluorescent tag In molecular biology and biotechnology, a fluorescent tag, also known as a fluorescent label or fluorescent pr ...

ethidium bromide
) or other elements modifying the stiffness of the DNA. *''W'' = writhe - number of turns of the double stranded DNA helix around the superhelical axis *''L'' = ''T'' + ''W'' and Δ''L'' = Δ''T'' + Δ''W'' Any change of T in a closed topological domain must be balanced by a change in W, and vice versa. This results in higher order structure of DNA. A circular DNA molecule with a writhe of 0 will be circular. If the twist of this molecule is subsequently increased or decreased by supercoiling then the writhe will be appropriately altered, making the molecule undergo plectonemic or toroidal superhelical coiling. When the ends of a piece of double stranded helical DNA are joined so that it forms a circle the strands are topologically knotted. This means the single strands cannot be separated any process that does not involve breaking a strand (such as heating). The task of un-knotting topologically linked strands of DNA falls to enzymes termed
topoisomerase Topoisomerases (or DNA topoisomerases) are enzymes that participate in the overwinding or underwinding of DNA. The winding problem of DNA arises due to the intertwined nature of its double-helical structure. During DNA replication and transcriptio ...
s. These enzymes are dedicated to un-knotting circular DNA by cleaving one or both strands so that another double or single stranded segment can pass through. This un-knotting is required for the replication of circular DNA and various types of recombination in linear DNA which have similar topological constraints.


The linking number paradox

For many years, the origin of residual supercoiling in eukaryotic genomes remained unclear. This topological puzzle was referred to by some as the "linking number paradox". However, when experimentally determined structures of the
nucleosome A nucleosome is the basic structural unit of DNA Deoxyribonucleic acid (; DNA) is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon ...

nucleosome
displayed an over-twisted left-handed wrap of DNA around the
histone In biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanisms ...
octamer, this ''paradox'' was considered to be solved by the scientific community.


See also

*
Triple-stranded DNA Triple-stranded DNA (also known as H-DNA or Triplex-DNA) is a DNA structure in which three oligonucleotides wind around each other and form a triple helix. In triple-stranded DNA, the third strand binds to a Nucleic acid double helix#Helix geometr ...
*
G-quadruplex In molecular biology, G-quadruplex secondary structures (G4) are formed in nucleic acids by sequences that are rich in guanine Guanine () (symbol A symbol is a mark, sign, or word In linguistics, a word of a spoken language can be defin ...

G-quadruplex
*
DNA nanotechnology DNA nanotechnology is the design and manufacture of artificial nucleic acid structures for technological uses. In this field, nucleic acids are used as non-biological engineering materials for nanotechnology rather than as the carriers of genetic ...
* Molecular models of DNA *
Molecular structure of Nucleic Acids "Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid" was the first article scientific literature, published to describe the discovery of the double helix structure of DNA, using X-ray diffraction and the mathematics of ...
(publication) *
Comparison of nucleic acid simulation software This is a list of notable computer programs that are used for nucleic acid Nucleic acids are biopolymer Biopolymers are natural polymer A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, ...


References

{{Biomolecular structure DNA Biophysics
Molecular structure A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral group of two or more atom An atom is the smallest unit of ordinary matter In ...
Helices