Conformational transitions in closed circular DNA molecules. I. Topological and energetical considerations.

A theory of conformational transitions in closed circular DNA as a function of topological linking number of the molecule (alpha) is elaborated taking into account topological and energetical considerations. The theory predicts a step-like dependence of a number of superhelical turns in DNA molecules (tau) on delta alpha. Thus, the number of superhelical turns tau = delta alpha for small values of delta alpha. For a large delta alpha (when conformational begin to occur) tau = delta alpha - sigma phi ij, where sigma phi ij is the total angle of conformational transitions for a given delta alpha. This prediction is in good agreement with published data on the dependence of the sedimentation coefficient of circular DNA molecules on their topological linking number. The results also allow to explain the disagreement between a number of titratable superhelical turns in circular DNA molecules and a number of supercoiles seen on electron micrographs for molecules with sufficiently large delta alpha.