Ribbon theory
Encyclopedia
Topology
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...
that has seen particularly application as regards DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...
.
Concepts
- LinkLink (knot theory)In mathematics, a link is a collection of knots which do not intersect, but which may be linked together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory...
is the integer number of turns of the ribbon around its axis; - Twist is the rate of rotation of the ribbon around its axis;
- WritheWritheIn 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....
is a measure of non-planarity of the ribbon's axis curve.
Work by Călugăreanu, White and Brock Fuller led to the Călugăreanu–White–Fuller theorem that Link = Writhe + Twist.
See also
- Bollobás–Riordan polynomial
- Knots and graphsKnots and graphsKnots and graph theory are related in some simple ways.- Knot diagram :A knot in R3 , can be projected onto a plane R2 Knots and graph theory are related in some simple ways.- Knot diagram :A knot in R3 (respectively in the 3-sphere, S3), can be projected onto a plane R2 Knots and...
- Knot theoryKnot theoryIn topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
- DNA supercoilDNA supercoilDNA supercoiling refers to the over- or under-winding of a DNA strand, and is an expression of the strain on the polymer. Supercoiling is important in a number of biological processes, such as compacting DNA. Additionally, certain enzymes such as topoisomerases are able to change DNA topology to...