A superhelix is a molecular
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 structure in which a helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

 is itself coiled into a helix. This is significant to both protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s and gene
A gene is a molecular unit of heredity of a living organism. It is a name given to some stretches of DNA and RNA that code for a type of protein or for an RNA chain that has a function in the organism. Living beings depend on genes, as they specify all proteins and functional RNA chains...

tic material, such as overwound circular DNA
Circular DNA
Circular DNA is a form of DNA that is found in viruses, bacteria and archaea as well as in eukaryotic cells in the form of either mitochondrial DNA or plastid DNA....


The earliest significant reference in molecular biology
Molecular biology
Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...

 is from 1971, by F.B. Fuller:
A geometric invariant of a space curve, the writhing number, is defined and studied. For the central curve of a twisted cord the writhing number measures the extent to which coiling of the central curve has relieved local twisting of the cord. This study originated in response to questions that arise in the study of supercoiled double-stranded DNA rings.

About the writhing number, mathematician W.F. Pohl says:
It is well-known that the writhing number is a standard measure of the global geometry of a closed space curve.

Contrary to intuition a topological
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

 property, the linking number
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...

, arises from the geometric
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 properties twist and writhe according to the following relationship:
Lk = T + W,

where Lk is the linking number, W is the writhe
In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings....

 and T is the twist
Reidemeister move
In the mathematical area of knot theory, a Reidemeister move refers to one of three local moves on a link diagram. In 1926, Kurt Reidemeister and independently, in 1927, J.W. Alexander and G.B...

 of the coil.

The linking number refers to the number of times that one strand wraps around the other. In DNA this property does not change and can only be modified by specialized enzymes called topoisomerase
Topoisomerases are enzymes that regulate the overwinding or underwinding of DNA. The winding problem of DNA arises due to the intertwined nature of its double helical structure. For example, during DNA replication, DNA becomes overwound ahead of a replication fork...


External links

  • Calugareanu Theorem - From Wolfram Research's MathWorld
    MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at...

  • Writhe - From MathWorld.
  • Twist - From MathWorld.
  • DNA Structure and Topology at Molecular Biochemistry II: The Bello Lectures.
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