Distributions of circular DNA according its topological states

A distinctive feature of closed circular DNA molecules is their particular topological state, which cannot be altered by any conformational rearrangement short of breaking at least one strand. This topological constraint opens unique possibilities for experimental studies of the distributions of topological states created in different ways. Primarily, the equilibrium distributions of topological properties are considered in the review. It is described how such distributions can be obtained and measured experimentally, and how they can be computed. Comparison of the calculated and measured equilibrium distributions over the linking number of complementary strands, equilibrium fractions of knots and links formed by circular molecules has provided much valuable information about the properties of the double helix. Study of the steady-state fraction of knots and links created by type II DNA topoisomerases has revealed a surprising property of the enzymes: their ability to reduce these fractions considerably below the equilibrium level.