An elastic model for in-plane deformations of small DNA rings

In-plane deformations of an elastic ring are analyzed as a model for structural distortions of small covalently-closed DNA rings with little or no writhe. The static conformation of an unconstrained elastic ring is a geometric circle, but thermal fluctuations away from the circle are found to be significant. An elastic ring confined in a cylindrical pore of rigid radius less than the radius of the free ring is studied as a model for a small DNA ring in a tight resolving gel. The model is extended to include deformability of the pore. Larger rings are relatively more deformed in the pore than smaller ones. This result may be pertinent to the observation that at constant linking number the mobility of small DNA rings in a resolving gel decreases as the number of base pairs increases.