Monte carlo computation of the supercoiling energy,the sedimentation constant,and the radius of gyration of unknotted and knotted circular DNA

Closed random Gaussian polygonal chains of N (6 < N < 150) bonds of equal length b and thickness d have been generated on a computer. The knot type, the writhing number w, the radius of gyration, and the average of the inverse of the distance between two apices have been determined for each chain. For all the studied knot types—0, 3₁, 4₁, 5₁, and 5₂—the probability density of finding a given w is Gaussian. The Gaussian is centered about 0 for the amphichiral knots. Therefore, for long circular DNAs, the contribution to the supercoiling energy, which depends on w only, may be considered as purely entropic and may be expressed as ARTw²/N, in agreement with previous semiempirical considerations. The parameter A increases with chain thickness, it decreases as N gets larger but rapidly reaches a plateau. Comparison with experimental data from the literature would suggest that the ratio of the writhing to the constraint increases with ionic strength. The ratio of sedimentation constant of the supercoiled DNA to the sedimentation constant of the nicked DNA varies as N^1/4 (w/N)², and therefore depends on the writhing density and on the length of the DNA.