Twist, writhe, and geometry of a DNA loop containing equally spaced coplanar bends

The formation of a topologically closed DNA loop is important in many biological processes, including the regulation of transcription, recombination, and replication. Modeling DNA as an isotropic elastic rod, we use finite element analysis to show that the dependence of the twist (delta Tw) and the writhe (Wr) upon the linking number deficit (delta Lk) is strongly influenced by intrinsic bends. We determine how the geometry of a DNA loop changes as a function of the number of uniformly spaced coplanar 20 degrees bends, oriented so as to open toward the center of the loop. We also calculate the geometry of DNA rods that are smoothly bent to the same extent. The response of both delta Tw and Wr of a bent DNA to changes in delta Lk falls into one of three categories, depending upon the number of bends. For a single bend of 20 degrees, Wr increases monotonically with delta Lk and the change in delta Tw with distance is constant along the entire DNA axis. For two to ten 20 degrees bends, Wr passes first through a local maximum, then through a local minimum, and finally increases monotonically as delta Lk increases. For eleven to eighteen 20 degrees bends, Wr again varies monotonically with delta Lk. For all numbers of bends greater than two, the delta Tw per unit length depends upon the distribution of intrinsic bends, being constant between any two adjoining bends but varying with their position relative to the cut location. Accompanying these delta Lk-associated changes in Wr and delta Tw per unit length are characteristic changes in geometry that are specific for each category. The results of these calculations raise the possibility that intrinsic bends can serve as a control factor in the biological functions associated with loop formation in DNA.