supercoiling

Supercoiling refers to the coiling of a DNA double helix upon itself due to torsional stress in closed or constrained molecules. DNA has a topological property called the linking number (Lk), which in a relaxed, B-form molecule equals Lk0. When the molecule is over-wound, positive supercoiling occurs; when it is under-wound, negative supercoiling occurs. In practice, torsional strain is generated during processes such as DNA replication or transcription, where the movement of enzymes ahead of and behind a fork or RNA polymerase introduces twists that cannot be immediately relieved in constrained DNA.

Topologically, DNA twist (Tw) is the helical turns of the strands, and writhe (Wr) is the spatial coiling of the duplex. Lk = Tw + Wr. In closed circular DNA, Lk is constant unless a break occurs, so changes in Tw are offset by opposite changes in Wr, producing supercoils. Type I topoisomerases alter Lk by removing or adding a single helical turn; type II enzymes alter Lk by steps of two and often introduce supercoils using ATP. Bacterial gyrase is a type II topoisomerase that introduces negative supercoils.

Biological roles and regulation: negative supercoiling facilitates strand separation needed for transcription and replication and contributes to chromatin compaction in eukaryotes. Cells actively regulate global supercoiling through topoisomerases, gyrase, and other factors; supercoiling level is described by superhelical density sigma.

Measurement and observation: methods such as gel electrophoresis, two-dimensional gel assays, and intercalator experiments distinguish supercoiled from relaxed DNA. In vivo, chromatin organization modulates effective supercoiling and can respond to environmental conditions.