Descriptive properties associated with supercoiling

DNA Supercoiling as a Pattern for Understanding Psycho-social (Part #4)

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"Supercoiling" is an abstract mathematical property, and represents the sum of what are termed "twist" and "writhe". "Supercoil" is seldom used as a noun with reference to DNA topology. It is the combination of twists and writhes that impart the supercoiling, and these occur in response to a change in the linking number. A coiled structure is at a higher energy (less stable). When the linking number is reduced in closed circular DNA, the molecule supercoils by minimizing twisting and bending. To partially relieve the strain introduced by the change in linking number (a 'deficit' in the link), the DNA must distort in other ways -- compensating with a change in twist or writhe. These are, physically, the two ways that the DNA can do so. The relationship of twist, writhe and supercoiling is expressed by the equation S = T + W (known as White's formula). Twist and writhe are geometric quantities. Unusually, link as a topological property is equal to the sum of two geometric properties. Their values change if the ribbon is deformed in space. Link, twist and writhe can be either positive or negative. Link is always an integer, whereas twist and writhe can take any real values.

• Writhing: Global contortions of circular DNA are described as "writhe". The writhing number describes the supertwisting or supercoiling of the helix in space. It is the number of turns that the duplex axis makes about the superhelix axis. Writhe describes the supercoiling, the coiling of the DNA coil. It is a measure of the DNA's superhelicity (supercoiling) and can be positive or negative. Writhe is a measure of the coiling, bending or non-planarity of the axis of the double helix. A right-handed coil is assigned a negative number (negative supercoiling) and a left-handed coil is assigned a positive number (positive supercoiling). When a molecule is relaxed and contains no supercoils, the linking number = the twist number since W= 0 The linking number of relaxed DNA is L 0 L 0 = N/10.5, where N is the number of base pairs in the DNA fragment.
  
  
• Twisting: Twist is the number of helical turns in the DNA, i.e., the complete revolutions that one polynucleotide strand makes about the duplex axis in the particular conformation under consideration. Twist is normally the number of base pairs divided by 10.4, that is the number of bases per turn of the helix. Twist is altered by deformation and is a local phenomenon. The total twist is the sum of all of the local twists. Twist is a measure of deformation due to a twisting motion.
  Twist and writhe are interconvertable. 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.
  
  
• Linking number: This is a topological property that determines the degree of supercoiling; It defines the number of times a strand of DNA winds in the right-handed direction around the helix axis when the axis is constrained to lie in a plane. It is the number of times that one DNA strand crosses about the other when the DNA is made to lie flat on a plane. If both strands are covalently intact, the linking number cannot change. Link is thus a topological invariant, remaining unaltered even if the two curves are deformed in space -- as long as neither is cut. Topology theory indicates that the sum of T and W equals to linking number: L=T+W. For example, in the circular DNA of 5400 basepairs, the linking number is 5400/10=540. When a molecule is relaxed and contains no supercoils, the linking number = the twist number since W= 0. Thus if there is no supercoiling, then W=0, T=L=540. If there is positive supercoiling, W=+20, T=L-W=520. In the special cases in which axis of the double helix remains in a plane or on the surface of a sphere, then twist equals the linking number, and there is no writhe, but all other cases are considerably more complex. Supercoiling can be caused even by an increase in the linking number (though this does not occur in nature).
  
  
• Density: the density of supercoiling.is useful to define as a property that distinguishes DNAs varying significantly in size. Superhelical density is the number of supercoils per turn of helix. It is denoted by the Greek letter sigma. It is defined as the number of turns that have been added or subtracted in the supercoiled DNA, compared to the relaxed state, divided by the total number of turns in the DNA if it were relaxed (which would normally be bp/10.5). Typically, sigma is between -.05 and -.07 (5-7% underwinding) in isolated natural DNA
  
  
• Link altering enzymes: The functionality of DNA is related to its topology which is maintained by enzymes that are capable of altering it. Nature has come up with particular enzymes that control the knottedness (as well as other topological states such as twist-induced supercoiling) of DNA. The exact ability of these enzymes to locate a knot in a circular DNA is an unresolved question in molecular biology. Known as Topoisomerases, these enzymes change the structure by altering the DNA link of a molecule. This is achieved by temporarily breaking one of the strands, passing the other strand through it, and then resealing the bonds. This effectively changes the linking number in the DNA. The enzymes are of two types:
  • Type-1: function by creating transient single-strand breaks in DNA, altering the link by one, by cutting one strand and passing the other strand through the break.
  • Type-2: alter the link by two, by breaking both the strands of the double helix at the same time and passing a segment of the double helix through the break.
  Many topoisomerase enzymes sense supercoiling and either generate or dissipate it as they change DNA topology.
  
  
• Replication: Level of supercoiling is known to be important for initiation of replication. In DNA replication, the two strands of DNA have to be separated, which leads either to overwinding of surrounding regions of DNA or to supercoiling. During replication, only part of the DNA unwinds (200 bps) while the rest of the DNA still remain configured at 10 bps per turn. A specialized set of enzymes (gyrase, topoisomerases) is present to introduce supercoils that favor strand separation; The degree of supercoils can be quantitatively described. Because of the wound configuration of DNA, biochemical transactions requiring strand separation necessitate chromosome movement (spin) about the long axis of the DNA. DNA replication, recombination and transcription all require DNA rotation. During DNA synthesis the rotation speed approaches 6000 rpm.
  
  
• DNA Replication, RNA transcription, and Gene expression: Negative supercoiling in cells is energetically unfavorable and must be introduced in some manner: Therefore transcription is supercoil dependent. Topological domains may thus alter local regulation of gene expression. The overall level of supercoiling in a cell could have a global effect on gene expression. DNA is transcribed into mRNA in the nucleus. There are particular codons to which the enzymes are begin the transcription. The mRNA travels to, and attaches itself to a ribosome. There, the nucleotides are read from the start codon, in three letter sections, each of which code for a particular amino acid (some amino acids have multiple codons that code for them). The tRNA brings amino acids from the surrounding cytosol to the ribosome, and attach them in the order coded by the mRNA. The amino acids are then bonded together by peptide bonds. They are in a long linear chain, which is the primary conformation. The conformation to secondary structure is usually spontaneous, based on the interactions between the amino acids within the polypeptide. However, when going to the tertiary and quarternary conformations, there are usually larger proteins called chaperones that assist in the folding.
  
  

• Denaturation, melting, breathing and unzipping: A physical property cricual to the function of DNA in replication and trqnscription is the ease with which its component parts can separate and be rejoined. This process is sometimes referred to as "melting" and "reannealing", or "denaturation" and "renaturation". DNA denaturation (or "melting") is due to the breakage of the hydrogen bonds in the Watson-Crick base-pairs, and is therefore reversible. This "unzipping" can be brought about by several processes. Under physiological conditions, local DNA-breathing occurs spontaneously due to thermal fluctuations. This opens up transient bubbles of a few tens of base pairs. These breathing fluctuations may be supported by single-strand binding proteins, thereby lowering the DNA base pair stability. DNA breathing and the lability of local stretches of the DNA double-helix is essential for numerous physiological processes such as the association of single-strand binding proteins, and the initiation of replication and transcription. (see Ralf Metzler and Andreas Hanke. Knots, bubbles, untying, and breathing: probing the topology of DNA and other biomolecules. 2004). [more | more]
  
  

• DNA-knots: DNA knots can arise in various biological reactions involving circular DNA molecules. Site specific recombination enzymes are known to produce specific families of knots. Identification of the knot types indicates the mechanism of action of a given enzyme and the overall shape of supercoiled circular DNA molecules at the moment of knotting [more | more]. Internal pairing in short single-stranded DNA can be utilised for the construction of different types of DNA knots [images]. The presence of knots inhibits the assembly of chromatin. Knotted chromosomes cannot be separated during mitosis, and knots in a chromosome may serve as topological barriers between different sections of chromosomes, such that the genomic structural organisation is altered.

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