Abstract
This paper analyzes equilibrium superhelical cruciform formation in a topologial domain of DNA containing inverted repeat sequences. The cruciform conformation is shown to be stable when the molecule is sufficiently negatively supercoiled but not when it is positively supercoiled. For a particular sequence containing a single inverted repeat, onset of stability occurs at a degree of negative superhelicity that depends critically on the number of base pairs separating the repeat copies. The free energy associated with the stable cruciform state is constant, independent of the degree of superhelicity, up to the point where the complete inverted repeat participates in the cruciform. In contrast, the free energy of the alternative, unextruded state grows approximately quadratically with the superhelical deformation. Therefore, a degree of negative supercoiling occurs at which the cruciform state becomes energetically favored. The equilibrium properties of this cruciform extrusion transition vary with segment length, the positions and sizes of the inverted repeats involved, environmental conditions, and the degree of superhelicity imposed. In a segment containing multiple repeats, both tandem and inverted, of one or more sequences, the pattern of cruciforms that form is dependent on superhelicity in a complex way. Specific cruciforms may occur at equilibrium only in narrow ranges of superhelicity, their reabsorption being coupled to the extrusion of others.