DNA supercoiling refers to the over- or under-winding of a DNA strand,
and is an expression of the strain on that strand. Supercoiling is
important in a number of biological processes, such as compacting DNA,
and by regulating access to the genetic code, DNA supercoiling
strongly affects DNA metabolism and possibly gene expression.
Additionally, certain enzymes such as topoisomerases are able to
1 Overview 2 Visualizing DNA supercoils: Intercalation-induced supercoiling of DNA 3 Functions
3.1 Genome packaging 3.2 Gene expression
4 Mathematical description 5 Effects on sedimentation coefficient 6 See also 7 References
7.1 General references
In a "relaxed" double-helical segment of B-DNA, the two strands twist
around the helical axis once every 10.4–10.5 base pairs of sequence.
Adding or subtracting twists, as some enzymes can do, imposes strain.
If a DNA segment under twist strain were closed into a circle by
joining its two ends and then allowed to move freely, the circular DNA
would contort into a new shape, such as a simple figure-eight. Such a
contortion is a supercoil. The noun form "supercoil" is often used in
the context of DNA topology.
Positively supercoiled (overwound) DNA is transiently generated during
Drawing showing the difference between a circular DNA chromosome (a plasmid) with a secondary helical twist only, and one containing an additional tertiary superhelical twist superimposed on the secondary helical winding.
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 Lk. The linking number is the most descriptive property of supercoiled DNA. Lko, 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.
= b p
displaystyle Lk_ o =bp/10.4
Lk is merely the number of crosses a single strand makes across the other. Lk, known as the "linking number", is 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.
L k = T w + W r
Tw, called "twist", refers to 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, ΔLk, is the actual number of turns in the plasmid/molecule, Lk, minus the number of turns in the relaxed plasmid/molecule Lko.
L k = L k − L
displaystyle Delta Lk=Lk-Lk_ o
If the DNA is negatively supercoiled ΔLk < 0. 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, that 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.
σ = Δ
displaystyle sigma =Delta Lk/Lk_ o
Gibbs free energy
N = 10 R T
displaystyle Delta G/N=10RTsigma ^ 2
The difference in
Gibbs free energy
N = 700 K c a l
b p ∗ ( Δ L k
displaystyle Delta G/N=700Kcal/bp*(Delta Lk/N)
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) L0 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.
T = 0, W = 0, then L = 0 T = +3, W = 0, then L = +3 T = +2, W = +1, then L = +3
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, DNA replication, and recombination.
Negative supercoiling is also thought to favour the transition between
Figure showing the various conformational changes which are observed in circular DNA at different pH. At a pH of about 12 (alkaline), there is a dip in the sedimentation coefficient, followed by a relentless increase up to a pH of about 13, at which pH the structure converts into the mysterious "Form IV".
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 Lk 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 Ribbon theory
^ Bar, A.; Mukamel, D.; Kabakçoǧlu, A. (2011). "Denaturation of
circular DNA: Supercoil mechanism". Physical Review E. 84 (4).
^ Champoux J (2001). "DNA topoisomerases: structure, function, and
mechanism". Annu Rev Biochem. 70: 369–413.
doi:10.1146/annurev.biochem.70.1.369. PMID 11395412.
^ a b c d e f Singer, Emily (5 January 2016). "How Strange Twists in
DNA Orchestrate Life". Quanta Magazine. Retrieved 2016-01-07.
^ a b c d e Irobalieva, Rossitza N.; Zechiedrich, Lynn; et al. (12
October 2015). "Structural diversity of supercoiled DNA". Nature
Communications. 6 (8440). doi:10.1038/ncomms9440. PMC 4608029 .
PMID 26455586. Retrieved 2016-01-07.
^ Ganji, Mahipal; Kim, Sung Hyun; van der Torre, Jaco; Abbondanzieri,
Elio; Dekker, Cees (2016-07-13). "Intercalation-Based Single-Molecule
Bloomfield, Victor A.; Crothers, Donald M.; Tinoco, Jr., Ignacio (2000). Nucleic acids: structures, properties, and functions. Sausalito, California: University Science Books. pp. 446–453. ISBN