Because of the double-helical structure of DNA, in which two strands of complementary nucleotides intertwine around each other, a covalently closed DNA molecule with no interruptions in either strand can be viewed as two interlocked single-stranded rings. Two closed space curves have long been known by mathematicians to exhibit a property called the linking number, a topologically invariant integer. During the 1960’s the linking number was shown to be the sum of two other quantities, the twist of one of the curves about the other, and the writhing number, or writhe, a measure of the chiral distortion from planarity of one of the two closed curves. In the case of DNA, the twist gives information about the secondary structure of the molecule, the winding of a helical strand about the double helical axis, and the writhe is associated with the supercoiling (tertiary structure) of the axis itself. We have been concerned with the form of expressions for the twist and writhe consistent with the modern view of DNA as a sequence of base-pair steps. Structural biologists commonly characterize the spatial disposition of each step in terms of six rigid-body parameters, one of which, coincidentally, is also called the twist. Of interest is the difference in the mathematical properties between this step-parameter twist and the twist of supercoiling associated with a given base-pair step. For example, it turns out that the latter twist, unlike the former, is sensitive to translational shearing distortions of the molecule that are chiral in nature. Thus, by comparing the values for the two twists for each step of a high-resolution structure of a protein-DNA complex, we can determine how the binding of various proteins contributes to the supercoiling of the DNA.