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 of a strand’s supercoiling affects a number of biological processes, such as compacting DNA and regulating access to the genetic code (which strongly affects
DNA metabolism and possibly gene expression). Certain enzymes, such as
topoisomerase
DNA topoisomerases (or topoisomerases) are enzymes that catalyze changes in the topological state of DNA, interconverting relaxed and supercoiled forms, linked (catenated) and unlinked species, and knotted and unknotted DNA. Topological issues i ...
s, change the amount of DNA supercoiling to facilitate functions such as
DNA replication
In molecular biology, DNA replication is the biological process of producing two identical replicas of DNA from one original DNA molecule. DNA replication occurs in all living organisms acting as the most essential part for biological inheritanc ...
and
transcription
Transcription refers to the process of converting sounds (voice, music etc.) into letters or musical notes, or producing a copy of something in another medium, including:
Genetics
* Transcription (biology), the copying of DNA into RNA, the fir ...
. The amount of supercoiling in a given strand is described by a mathematical formula that compares it to a reference state known as "relaxed B-form" DNA.
Overview
In a "relaxed"
double-helical segment of
B-DNA, the two strands twist around the helical axis once every 10.4–10.5
base pair
A base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both DNA ...
s of
sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...
. Adding or subtracting twists, as some
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. A ...
s do, imposes strain. If a DNA segment under twist strain is closed into a circle by joining its two ends, and then allowed to move freely, it takes on different shape, such as a figure-eight. This shape is referred to as a supercoil. (The noun form "supercoil" is often used when describing
DNA topology
Nucleic acid structure refers to the structure of nucleic acids such as DNA and RNA. Chemically speaking, DNA and RNA are very similar. Nucleic acid structure is often divided into four different levels: primary, secondary, tertiary, and quat ...
.)
The DNA of most organisms is usually negatively supercoiled. It becomes temporarily positively supercoiled when it is being replicated or transcribed. These processes are inhibited (regulated) if it is not promptly relaxed. The simplest shape of a supercoil is a figure eight; a circular DNA strand assumes this shape to accommodate more or few helical twists. The two lobes of the figure eight will appear rotated either clockwise or counterclockwise with respect to one another, depending on whether the helix is over- or underwound. For each additional helical twist being accommodated, the lobes will show one more rotation about their axis.
Lobal contortions of a circular DNA, such as the rotation of the figure-eight lobes above, are referred to as ''
writhe
In knot theory, there are several competing notions of the quantity writhe, or \operatorname. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amou ...
''. The above example illustrates that twist and writhe are interconvertible. Supercoiling can be represented mathematically by the sum of twist and writhe. The twist is the number of helical turns in the DNA and the writhe is the number of times the double helix crosses over on itself (these are the supercoils). Extra helical twists are positive and lead to positive supercoiling, while subtractive twisting causes negative supercoiling. Many
topoisomerase
DNA topoisomerases (or topoisomerases) are enzymes that catalyze changes in the topological state of DNA, interconverting relaxed and supercoiled forms, linked (catenated) and unlinked species, and knotted and unknotted DNA. Topological issues i ...
enzymes sense supercoiling and either generate or dissipate it as they change DNA topology.
In part because
chromosome
A chromosome is a long DNA molecule with part or all of the genetic material of an organism. In most chromosomes the very long thin DNA fibers are coated with packaging proteins; in eukaryotic cells the most important of these proteins are ...
s may be very large, segments in the middle may act as if their ends are anchored. As a result, they may be unable to distribute excess twist to the rest of the chromosome or to absorb twist to recover from underwinding—the segments may become ''supercoiled'', in other words. In response to supercoiling, they will assume an amount of writhe, just as if their ends were joined.
Supercoiled DNA forms two structures; a plectoneme or a toroid, or a combination of both. A negatively supercoiled DNA molecule will produce either a one-start left-handed helix, the toroid, or a two-start right-handed helix with terminal loops, the plectoneme. Plectonemes are typically more common in nature, and this is the shape most bacterial
plasmid
A plasmid is a small, extrachromosomal DNA molecule within a cell that is physically separated from chromosomal DNA and can replicate independently. They are most commonly found as small circular, double-stranded DNA molecules in bacteria; how ...
s will take. For larger molecules it is common for hybrid structures to form – a loop on a toroid can extend into a plectoneme. If all the loops on a toroid extend then it becomes a branch point in the plectonemic structure. DNA supercoiling is important for DNA packaging within all cells, and seems to also play a role in gene expression.
Intercalation-induced supercoiling of DNA
Based on the properties of
intercalating molecules, i.e.
fluorescing
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
upon binding to DNA and unwinding of DNA base-pairs, in 2016, a
single-molecule technique has been introduced to directly visualize individual plectonemes along supercoiled DNA which would further allow to study the interactions of DNA processing proteins with supercoiled DNA. In that study, Sytox Orange (an intercalating dye) was used to induce supercoiling on surface tethered DNA molecules.
Using this
assay
An assay is an investigative (analytic) procedure in laboratory medicine, mining, pharmacology, environmental biology and molecular biology for qualitatively assessing or quantitatively measuring the presence, amount, or functional activity of a ...
, it was found that the DNA sequence encodes for the position of plectonemic supercoils. Furthermore, DNA supercoils were found to be enriched at the transcription start sites in
prokaryote
A prokaryote () is a single-celled organism that lacks a nucleus and other membrane-bound organelles. The word ''prokaryote'' comes from the Greek πρό (, 'before') and κάρυον (, 'nut' or 'kernel').Campbell, N. "Biology:Concepts & Connec ...
s.
Functions
Genome packaging
DNA supercoiling is important for DNA packaging within all cells. Because the length of DNA can be thousands of times that of a cell, packaging this genetic material into the cell or
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
*Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucle ...
(in
eukaryote
Eukaryotes () are organisms whose cells have a nucleus. All animals, plants, fungi, and many unicellular organisms, are Eukaryotes. They belong to the group of organisms Eukaryota or Eukarya, which is one of the three domains of life. Bacte ...
s) is a difficult feat. Supercoiling of DNA reduces the space and allows for DNA to be packaged. In prokaryotes, plectonemic supercoils are predominant, because of the circular chromosome and relatively small amount of genetic material. In eukaryotes, DNA supercoiling exists on many levels of both plectonemic and solenoidal supercoils, with the solenoidal supercoiling proving most effective in compacting the DNA. Solenoidal supercoiling is achieved with
histones
In biology, histones are highly basic proteins abundant in lysine and arginine residues that are found in eukaryotic cell nuclei. They act as spools around which DNA winds to create structural units called nucleosomes. Nucleosomes in turn are wr ...
to form a 10 nm fiber. This fiber is further coiled into a 30 nm fiber, and further coiled upon itself numerous times more.
DNA packaging is greatly increased during
mitosis
In cell biology, mitosis () is a part of the cell cycle in which replicated chromosomes are separated into two new nuclei. Cell division by mitosis gives rise to genetically identical cells in which the total number of chromosomes is mainta ...
when duplicated sister DNAs are segregated into daughter cells. It has been shown that
condensin
Condensins are large protein complexes that play a central role in chromosome assembly and segregation during mitosis and meiosis (Figure 1). Their subunits were originally identified as major components of mitotic chromosomes assembled in ''Xeno ...
, a large protein complex that plays a central role in mitotic chromosome assembly, induces positive supercoils in an
ATP hydrolysis-dependent manner ''in vitro''.
[ ][ ] Supercoiling could also play an important role during
interphase
Interphase is the portion of the cell cycle that is not accompanied by visible changes under the microscope, and includes the G1, S and G2 phases. During interphase, the cell grows (G1), replicates its DNA (S) and prepares for mitosis (G2). A c ...
in the formation and maintenance of
topologically associating domains (TADs).
Supercoiling is also required for
DNA/RNA synthesis. Because DNA must be unwound for DNA/RNA
polymerase
A polymerase is an enzyme ( EC 2.7.7.6/7/19/48/49) that synthesizes long chains of polymers or nucleic acids. DNA polymerase and RNA polymerase are used to assemble DNA and RNA molecules, respectively, by copying a DNA template strand using base- ...
action, supercoils will result. The region ahead of the polymerase complex will be unwound; this stress is compensated with positive supercoils ahead of the complex. Behind the complex, DNA is rewound and there will be compensatory negative supercoils.
Topoisomerases
DNA topoisomerases (or topoisomerases) are enzymes that catalyze changes in the topological state of DNA, interconverting relaxed and supercoiled forms, linked (catenated) and unlinked species, and knotted and unknotted DNA. Topological issues i ...
such as
DNA gyrase
DNA gyrase, or simply gyrase, is an enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrat ...
(Type II Topoisomerase) play a role in relieving some of the stress during DNA/RNA synthesis.
Gene expression
Specialized proteins can unzip small segments of the DNA molecule when it is replicated or
transcribed into
RNA
Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
. But work published in 2015 illustrates how DNA opens on its own.
Simply twisting DNA can expose internal bases to the outside, without the aid of any proteins. Also, transcription itself contorts DNA in living human cells, tightening some parts of the coil and loosening it in others. That stress triggers changes in shape, most notably opening up the helix to be read. Unfortunately, these interactions are very difficult to study because biological molecules morph shapes so easily. In 2008 it was noted that transcription twists DNA, leaving a trail of undercoiled (or negatively supercoiled) DNA in its wake. Moreover, they discovered that the DNA sequence itself affects how the molecule responds to supercoiling.
For example, the researchers identified a specific sequence of DNA that regulates transcription speed; as the amount of supercoil rises and falls, it slows or speeds the pace at which molecular machinery reads DNA.
It is hypothesized that these structural changes might trigger stress elsewhere along its length, which in turn might provide trigger points for replication or gene expression.
This implies that it is a very dynamic process in which both DNA and proteins each influences how the other acts and reacts.
Gene Expression during cold shock
Almost half of the genes of the bacterium E. coli that are repressed during cold shock are similarly repressed when Gyrase is blocked by the antibiotic Novobiocin.
Moreover, during cold shocks, the density of nucleoids increases, and the protein gyrase and the nucleoid become colocalized (which is consistent with a reduction in DNA relaxation). This is evidence that the reduction of negative supercoiling of the DNA is one of the main mechanisms responsible for the blocking of transcription of half of the genes that conduct the cold shock transcriptional response program of bacteria. Based on this, a stochastic model of this process has been proposed. This model is illustrated in the figure, where reactions 1 represent transcription and its locking due to supercoiling. Meanwhile, reactions 2 to 4 model, respectively, translation, and RNA and protein degradation.
Mathematical description
In nature, circular DNA is always isolated as a higher-order helix-upon-a-helix, known as a ''superhelix''. In discussions of this subject, the Watson–Crick twist is referred to as a "secondary" winding, and the superhelices as a "tertiary" winding. The sketch at right indicates a "relaxed", or "open circular" Watson–Crick double-helix, and, next to it, a right-handed superhelix. The "relaxed" structure on the left is not found unless the chromosome is nicked; the superhelix is the form usually found in nature.
For purposes of mathematical computations, a right-handed superhelix is defined as having a "negative" number of superhelical turns, and a left-handed superhelix is defined as having a "positive" number of superhelical turns. In the drawing (shown at the right), both the secondary (''i.e.,'' "Watson–Crick") winding and the tertiary (''i.e.,'' "superhelical") winding are right-handed, hence the supertwists are negative (–3 in this example).
The superhelicity is presumed to be a result of underwinding, meaning that there is a deficiency in the number of secondary Watson–Crick twists. Such a chromosome will be strained, just as a macroscopic metal spring is strained when it is either overwound or unwound. In DNA which is thusly strained, supertwists will appear.
DNA supercoiling can be described numerically by changes in the
linking number
In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. In E ...
''Lk''. The linking number is the most descriptive property of supercoiled DNA. ''Lk
o'', the number of turns in the relaxed (B type) DNA plasmid/molecule, is determined by dividing the total base pairs of the molecule by the relaxed
bp/turn which, depending on reference is 10.4;
10.5;
10.6.
:
''Lk'' is the number of crosses a single strand makes across the other, often visualized as the number of Watson–Crick twists found in a circular chromosome in a (usually imaginary) planar projection. This number is physically "locked in" at the moment of covalent closure of the chromosome, and cannot be altered without strand breakage.
The topology of the DNA is described by the equation below in which the linking number is equivalent to the sum of ''Tw'', which is the number of twists or turns of the double helix, and ''Wr'', which is the number of coils or "writhes." If there is a closed DNA molecule, the sum of ''Tw'' and ''Wr'', or the linking number, does not change. However, there may be complementary changes in ''Tw'' and ''Wr'' without changing their sum:
:
''Tw'', called "twist," is the number of Watson–Crick twists in the chromosome when it is not constrained to lie in a plane. We have already seen that native DNA is usually found to be superhelical. If one goes around the superhelically twisted chromosome, counting secondary Watson–Crick twists, that number will be different from the number counted when the chromosome is constrained to lie flat. In general, the number of secondary twists in the native, supertwisted chromosome is expected to be the "normal" Watson–Crick winding number, meaning a single 10-base-pair helical twist for every 34 Å of DNA length.
''Wr'', called "writhe," is the number of superhelical twists. Since biological circular DNA is usually underwound, ''Lk'' will generally be ''less'' than ''Tw'', which means that ''Wr'' will typically be ''negative.''
If DNA is underwound, it will be under strain, exactly as a metal spring is strained when forcefully unwound, and that the appearance of supertwists will allow the chromosome to relieve its strain by taking on negative supertwists, which correct the secondary underwinding in accordance with the topology equation above.
The topology equation shows that there is a one-to-one relationship between changes in ''Tw'' and ''Wr''. For example, if a secondary "Watson–Crick" twist is removed, then a right-handed supertwist must have been removed simultaneously (or, if the chromosome is relaxed, with no supertwists, then a left-handed supertwist must be added).
The change in the linking number, Δ''Lk'', is the actual number of turns in the plasmid/molecule, ''Lk'', minus the number of turns in the relaxed plasmid/molecule ''Lk
o'':
:
If the DNA is negatively supercoiled,
. The negative supercoiling implies that the DNA is underwound.
A standard expression independent of the molecule size is the "specific linking difference" or "superhelical density" denoted ''σ'', which represents the number of turns added or removed relative to the total number of turns in the relaxed molecule/plasmid, indicating the level of supercoiling.
:
The
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...
associated with the coiling is given by the equation below
:
The difference in
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...
between the supercoiled circular DNA and uncoiled circular DNA with ''N'' > 2000 bp is approximated by:
:
or, 16 cal/bp.
Since the linking number ''L'' of supercoiled DNA is the number of times the two strands are intertwined (and both strands remain covalently intact), ''L'' cannot change. The reference state (or parameter) ''L
0'' of a circular DNA duplex is its relaxed state. In this state, its writhe ''W'' = 0. Since ''L = T + W'', in a relaxed state ''T = L''. Thus, if we have a 400 bp relaxed circular DNA duplex, ''L ~ 40'' (assuming ~10 bp per turn in B-DNA). Then ''T ~ 40''.
*Positively supercoiling:
*:T = 0, W = 0, then L = 0
*:T = +3, W = 0, then L = +3
*:T = +2, W = +1, then L = +3
*Negatively supercoiling:
*:T = 0, W = 0, then L = 0
*:T = -3, W = 0, then L = -3
*:T = -2, W = -1, then L = -3
Negative supercoils favor local unwinding of the DNA, allowing processes such as
transcription
Transcription refers to the process of converting sounds (voice, music etc.) into letters or musical notes, or producing a copy of something in another medium, including:
Genetics
* Transcription (biology), the copying of DNA into RNA, the fir ...
,
DNA replication
In molecular biology, DNA replication is the biological process of producing two identical replicas of DNA from one original DNA molecule. DNA replication occurs in all living organisms acting as the most essential part for biological inheritanc ...
, and
recombination. Negative supercoiling is also thought to favour the transition between 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 form. Z-DNA is thought ...
, and moderate the interactions of DNA binding proteins involved in
gene regulation
Regulation of gene expression, or gene regulation, includes a wide range of mechanisms that are used by cells to increase or decrease the production of specific gene products (protein or RNA). Sophisticated programs of gene expression are wide ...
.
Stochastic models
Some stochastic models have been proposed to account for the effects of positive supercoiling buildup (PSB) in gene expression dynamics (e.g. in bacterial gene expression), differing in, e.g., the level of detail. In general, the detail increases when adding processes affected by and affecting supercoiling. As this addition occurs, the complexity of the model increases.
For example, in
two models of different complexity are proposed. In the most detailed one, events were modeled at the nucleotide level, while in the other the events were modeled at the promoter region alone, and thus required much less events to be accounted for.
Examples of stochastic models that focus on the effects of PSB on a promoter’s activity can be found in:
. In general, such models include a promoter, Pro, which is the region of DNA controlling transcription and, thus, whose activity/locking is affected by PSB. Also included are RNA molecules (the product of transcription), RNA polymerases (RNAP) which control transcription, and Gyrases (G) which regulate PSB. Finally, there needs to be a means to quantify PSB on the DNA (i.e. the promoter) at any given moment. This can be done by having some component in the system that is produced over time (e.g., during transcription events) to represent positive supercoils, and that is removed by the action of Gyrases. The amount of this component can then be set to affect the rate of transcription.
Effects on sedimentation coefficient
The topological properties of circular DNA are complex. In standard texts, these properties are invariably explained in terms of a helical model for DNA, but in 2008 it was noted that each topoisomer, negative or positive, adopts a unique and surprisingly wide distribution of three-dimensional conformations.
When the sedimentation coefficient, ''s'', of circular DNA is ascertained over a large range of
pH, the following curves are seen. Three curves are shown here, representing three species of DNA. From top-to-bottom they are: "Form IV" (green), "Form I" (blue) and "Form II" (red).
"Form I" (blue curve) is the traditional nomenclature used for the native form of duplex circular DNA, as recovered from viruses and intracellular plasmids. Form I is covalently closed, and any plectonemic winding which may be present is therefore locked in. If one or more nicks are introduced to Form I, free rotation of one strand with respect to the other becomes possible, and Form II (red curve) is seen.
Form IV (green curve) is the product of alkali denaturation of Form I. Its structure is unknown, except that it is persistently duplex, and extremely dense.
Between pH 7 and pH 11.5, the sedimentation coefficient ''s'', for Form I, is constant. Then it dips, and at a pH just below 12, reaches a minimum. With further increases in pH, ''s'' then returns to its former value. It doesn’t stop there, however, but continues to increase relentlessly. By pH 13, the value of ''s'' has risen to nearly 50, two to three times its value at pH 7, indicating an extremely compact structure.
If the pH is then lowered, the ''s'' value is not restored. Instead, one sees the upper, green curve. The DNA, now in the state known as Form IV, remains extremely dense, even if the pH is restored to the original physiologic range. As stated previously, the structure of Form IV is almost entirely unknown, and there is no currently accepted explanation for its extraordinary density. About all that is known about the tertiary structure is that it is duplex, but has no hydrogen bonding between bases.
These behaviors of Forms I and IV are considered to be due to the peculiar properties of duplex DNA which has been covalently closed into a double-stranded circle. If the covalent integrity is disrupted by even a single nick in one of the strands, all such topological behavior ceases, and one sees the lower Form II curve (Δ). For Form II, alterations in pH have very little effect on ''s''. Its physical properties are, in general, identical to those of linear DNA. At pH 13, the strands of Form II simply separate, just as the strands of linear DNA do. The separated single strands have slightly different ''s'' values, but display no significant changes in ''s'' with further increases in pH.
A complete explanation for these data is beyond the scope of this article. In brief, the alterations in ''s'' come about because of changes in the superhelicity of circular DNA. These changes in superhelicity are schematically illustrated by four little drawings which have been strategically superimposed upon the figure above.
Briefly, the alterations of ''s'' seen in the pH titration curve above are widely thought to be due to changes in the superhelical winding of DNA under conditions of increasing pH. Up to pH 11.5, the purported "underwinding" produces a right-handed ("negative") supertwist. But as the pH increases, and the secondary helical structure begins to denature and unwind, the chromosome (if we may speak anthropomorphically) no longer "wants" to have the full Watson–Crick winding, but rather "wants", increasingly, to be "underwound". Since there is less and less strain to be relieved by superhelical winding, the superhelices therefore progressively disappear as the pH increases. At a pH just below 12, all incentive for superhelicity has expired, and the chromosome will appear as a relaxed, open circle.
At higher pH still, the chromosome, which is now denaturing in earnest, tends to unwind entirely, which it cannot do so (because L
k is covalently locked in). Under these conditions, what was once treated as "underwinding" has actually now become "overwinding". Once again there is strain, and once again it is (in part at least) relieved by superhelicity, but this time in the opposite direction (''i.e.,'' left-handed or "positive"). Each left-handed tertiary supertwist removes a single, now ''undesirable'' right-handed Watson–Crick secondary twist.
The titration ends at pH 13, where Form IV appears.
See also
*
Mechanical properties of DNA
Mechanical may refer to:
Machine
* Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement
* Mechanical calculator, a device used to perform the basic operations of ...
*
Ribbon theory In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector. More formally, a ribbon denoted by (X,U) includes a curve X given by a three-dimensional vector X(s), depending continuou ...
References
General references
*{{cite book, last1=Bloomfield, first1=Victor A., last2=Crothers , first2=Donald M. , last3=Tinoco, Jr. , first3=Ignacio , title=Nucleic acids: structures, properties, and functions, year=2000, publisher=University Science Books, location=Sausalito, California, isbn=978-0935702491, pages=446–453
DNA
Helices
Molecular biology