DNA 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". The amount of a strand's supercoiling affects a number of biological processes, such as compacting DNA and regulating access to the genetic code. Certain enzymes, such as topoisomerases, change the amount of DNA supercoiling to facilitate functions such as DNA replication and transcription. 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 pairs of sequence. Adding or subtracting twists, as some enzymes 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 DNA of most organisms is usually negatively supercoiled. It becomes temporarily positively supercoiled when it is being replicated or transcribed. These processes are inhibited 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. 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. Extra helical twists are positive and lead to positive supercoiling, while subtractive twisting causes negative supercoiling. Many topoisomerase enzymes sense supercoiling and either generate or dissipate it as they change DNA topology.
In part because chromosomes 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 plasmids 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 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 was used to induce supercoiling on surface tethered DNA molecules.Using this assay, 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 prokaryotes.
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 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 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 when duplicated sister DNAs are segregated into daughter cells. It has been shown that condensin, 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 in the formation and maintenance of topologically associating domains.
Supercoiling is also required for DNA/RNA synthesis. Because DNA must be unwound for DNA/RNA polymerase 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 such as DNA gyrase play a role in relieving some of the stress during DNA/RNA synthesis.
In many bacterial species, barriers to supercoil diffusion divide the genome into a series of topologically isolated supercoil domains. These SDs play a major role in organizing the nucleoid. SDs negatively supercoiled on average but can sometimes be positively supercoiled as well. The degree of supercoiling can vary in response to different forms of stress and influences the binding of different nucleoid associated proteins that further organize the bacterial genome. For example, Dps from E. coli has been shown to bind supercoiled DNA much more rapidly that torsionally relaxed DNA.
Gene expression
Specialized proteins can unzip small segments of the DNA molecule when it is replicated or transcribed into RNA. 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 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. 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 on the left 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, both the secondary winding and the tertiary winding are right-handed, hence the supertwists are negative.
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 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 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.
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:
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 associated with the coiling is given by the equation below
The difference in Gibbs free energy 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, L cannot change. The reference state 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. 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