A theory of thermal fluctuations in DNA miniplasmids

A recent analysis of the normal modes of vibration of a ring formed by bringing together and sealing, with or without the addition of twist, the ends of rods that are straight when stress free is taken as the basis for a theory of the statistical thermodynamics of a canonical ensemble of DNA minicircles with specified linking number difference deltaLk and number N of base pairs. It is assumed that N corresponds to a circumference in the range of one or two persistence lengths. For such an ensemble, the theory yields an expression for the average writhe (Wr), which can be employed to calculate the free energy, entropy, and enthalpy of supercoiling, deltaGsc, deltaSsc, and deltaHsc. The results obtained for the dependence of deltaGsc on deltaLk and N are in accord with experimental observations of equilibrium distributions of topoisomers of plasmids with N approximately 200 bp.