DNA supercoiling and topology
Take a coiled telephone cord and twist one end: the cord itself starts to writhe and loop over on itself into bigger coils. DNA does the same. When the double helix is over- or under-wound, it relieves the strain by coiling upon itself — this higher-order twisting of the twist is called supercoiling.
DNA's two strands wind around each other a fixed number of times, and in a closed loop (like a bacterial chromosome) that number cannot change without breaking a strand. If a process such as replication or transcription over-winds the helix ahead of it, the molecule becomes positively supercoiled and tense; if it is under-wound, it becomes negatively supercoiled. Cells normally keep their DNA slightly negatively supercoiled, which makes the strands easier to pull apart. Topology is the branch of geometry describing exactly these unbreakable linking relationships in closed loops.
Supercoiling matters because every time the cell reads or copies DNA, it cranks more twist into the molecule, and that strain would quickly grind the machinery to a halt. The solution is a family of enzymes called topoisomerases (including bacterial gyrase) that transiently cut one or both strands, let the tension unwind, and reseal them. Because these enzymes are essential and bacteria-specific ones differ from ours, several antibiotics and anticancer drugs work by jamming topoisomerases.
Fluoroquinolone antibiotics like ciprofloxacin kill bacteria by trapping their topoisomerase (gyrase) mid-cut, so the broken DNA cannot be resealed; our human topoisomerases differ enough that the drug spares us.
Twist the twist — and topoisomerases relieve the strain.
Supercoiling is not just untidy tangling. It is a regulated, energy-carrying state: the right degree of negative supercoiling actually helps the cell open the helix where it needs to, so cells spend energy to maintain it, not merely to remove it.