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times, linked to other curves, and subjected to four or five successive orders of coiling to convert it into a compact form for information storage. If one scales the cell nucleus up to the size of a basketball, the DNA inside scales up to the size of thin fishing line, and 200 km of that fishing line are inside the nuclear basketball. Most cellular DNA is double-stranded (duplex), consisting of two linear backbones of alternating sugar and phosphorus. Attached to each sugar molecule is one of the four bases (nucleotides): A = adenine, T = thymine, C = cytosine, G = guanine. A ladder whose sides are the backbones and whose rungs are hydrogen bonds is formed by hydrogen bonding between base pairs, with A bonding only with T, and C bonding only with G. The base pair sequence for a linear segment of duplex DNA is obtained by reading along one of the two backbones, and is a word in the letters {A,T,C,G}. Due to the uniqueness of the bonding partner for each nucleotide, knowledge of the sequence along one backbone implies knowledge of the sequence along the other backbone. In the classical Crick-Watson double helix model for DNA, the ladder is twisted in a right-hand helical fashion, with an average and nearly constant pitch of approximately 10.5 base pairs per full helical twist. The local helical pitch of duplex DNA is a function of both the local base pair sequence and the cellular environment in which the DNA lives; if a DNA molecule is under stress, or constrained to live on the surface of a protein, or is being acted upon by an enzyme, the helical pitch can change. Duplex DNA can exist in nature in closed circular form, where the rungs of the ladder lie on a twisted cylinder. Circular duplex DNA exists in the mitochondria of human cells, for example. Duplex DNA in the cell nucleus is a linear molecule, one that is topologically constrained by periodic attachment to a protein scaffold in order to achieve efficient packing.

The packing, twisting, and topological constraints all taken together mean that topological entanglement poses serious functional problems for DNA. This entanglement would interfere with, and be exacerbated by, the vital life processes of replication, transcription, and recombination (Cozzarelli, 1992). For information retrieval and cell viability, some geometric and topological features must be introduced into the DNA, and others quickly removed (Wang, 1982, 1985). For example, the Crick-Watson helical twist of duplex DNA may require local unwinding in order to make room for a protein involved in