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The DNA Helix

The DNA Helix

Deoxyribonucleic acid, or DNA, is the genetic material responsible for passing traits from generation to generation in all organisms and most viruses. DNA is composed of two strands of nucleotides that wind around each other to form a spring-like structure called a double helix. However, the double helix is not perfectly symmetrical. Instead, there are regularly occurring grooves in the structure. The major groove occurs where the sugar-phosphate backbones are relatively far apart. This space...

The DNA Helix

The DNA Helix

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The DNA Helix

DNA as a Genetic Template

DNA as a Genetic Template

Two structural features of the DNA molecule provide a basis for the mechanisms of heredity: the four nucleotide bases and its double-stranded nature. The Watson-Crick model of double-helical DNA structure, proposed in 1952, drew heavily upon the X-ray crystallography work of researchers Rosalind Franklin and Maurice Wilkins. Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine for their work in 1962. Franklin was, controversially, excluded from the prize for...

DNA as a Genetic Template

DNA as a Genetic Template

Two structural features of the DNA molecule provide a basis for the mechanisms of heredity: the four nucleotide bases and its double-stranded nature. The Watson-Crick model of double-helical DNA structure, proposed in 1952, drew heavily upon the X-ray crystallography work of researchers Rosalind Franklin and Maurice Wilkins. Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine for their work in 1962. Franklin was, controversially, excluded from the prize for...

DNA Topoisomerases

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Topoisomerases are enzymes that relax overwound DNA molecules during various cell processes, including DNA replication and transcription. These enzymes regulate positive and negative DNA supercoiling without changing the nucleotide sequence. DNA overwinding in a clockwise direction results in positively supercoiled DNA, whereas underwinding in a counterclockwise direction produces negatively supercoiled DNA.
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Topoisomerases are divided into two main types. Type I...

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Related Experiment Video

Updated: May 13, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Framed curves and knotted DNA.

Gregory S Chirikjian¹

¹Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218 U.S.A.

Biochemical Society Transactions

|March 22, 2013

Summary

This review explores the geometry of framed curves and calculates twist and writhe in knotted DNA circles. It explains how bending relates to knot properties in closed curves.

Area of Science:

Mathematics and Molecular Biology
Computational Geometry
Biophysics

Background:

Knotted DNA structures are crucial for cellular processes.
Understanding DNA topology requires analyzing the geometry of these complex molecules.
Previous work has established links between curve geometry and knot invariants.

Purpose of the Study:

To review the local and global geometry of framed curves.
To detail the computation of twist and writhe in knotted DNA circles.
To explain classical inequalities connecting curve bending and knot parameters.

Main Methods:

Geometric analysis of framed curves.
Topological calculations of twist and writhe.
Review of established mathematical inequalities.

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Studying DNA Looping by Single-Molecule FRET

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Studying DNA Looping by Single-Molecule FRET

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Main Results:

Provides a framework for understanding the geometry of knotted DNA.
Details methods for quantifying DNA knot complexity.
Highlights relationships between physical properties (bending) and topological invariants.

Conclusions:

The geometry of framed curves is essential for analyzing DNA knots.
Twist and writhe are key computational measures for DNA topology.
Classical inequalities offer insights into the relationship between DNA bending and knotting.