Applications of the twist difference to DNA structural analysis.

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Abstract
The twist is a fundamental geometric property of nucleic acids. Calculation of the twist in the most general case requires detailed specification of the three-dimensional path of each strand, but many important cases may be analyzed by considering only the twist difference. If C1, C2, and C3 are three distinct space curves, the twist difference about C1 is defined as Tw(C3, C1) - Tw(C2, C1). We show here that this difference measures the rotation of the correspondence surface joining C1 to C2 about the correspondence surface joining C1 to C3. This result has application to DNA containing local nonuniformities, such as denatured regions, cruciforms, and other altered structures. It also facilitates the calculation of twist for three-stranded structures, including D-loops in mitochondrial DNA and replication and transcription intermediates. The twist difference may also be used to simplify greatly the analysis of twist changes in duplex DNA due to winding on surfaces, such as histones and certain enzymes. In such cases the strand-axis twist of DNA divides into two independent terms. The first term arises from the twist of the local reference frame, and the second arises from the rotation of either strand about the duplex axis as measured in the local reference frame. Twist changes consequent to nucleosome winding, for example, arise from the twist of the nucleosome axis, a straight line, about the DNA axis plus rotation of either strand of the DNA about its axis in the reference frame of the cylinder.

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