Knotting and supercoiling in circular DNA: A model incorporating the effect of added salt

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Abstract
We consider a model of a circular polyelectrolyte, such as DNA, in which the molecule is represented by a polygon in the three-dimensional simple cubic lattice. A short-range attractive force between nonbonded monomers is included (to account for solvent quality) together with a screened Coulomb potential (to account for the effect of added salt). We compute the probability that the ring is knotted as a function of the number of monomers in the ring, and of the ionic strength of the solution. The results show the same general behavior as recent experimental results by Shaw and Wang [Science 260, 533 (1993)] and by Rybenkov, Cozzarelli, and Vologodskii [Proc. Natl. Acad. Sci. U.S 90, 5307 (1993)] on the knot probability in circular DNA as a function of added salt. In addition, we compute the writhe of the polygon and show that this also increases as the ionic strength increases. The writhe computations model the conformational behavior of nicked circular duplex DNA molecules in salt solution.

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