Highly purified nicking-closing enzyme from mouse cells in 20-fold enzyme/substrate excess converts closed circular native PM2, ColEl, and Minicol DNA into limit product sets of DNAs. Each set has a mean degree of supercoiling of approximately zero. The individual species in the sets differ by Ar = i1, i42, etc., and the relative masses fit a Boltzmann distribution. It was also demonstrated that "nonsupercoiled" closed circular duplex molecules serve as substrates for the nicking-closing enzyme, and that a distribution of topological isomers is generated. Polynucleotide ligase, acting on nicked circular DNA, forms under the same conditions, the same set of closed DNAs. The latter enzyme freezes the population into sets of molecules otherwise in configurational equilibrium in solution.Nicking-closing (N-C) activities that alter the topological winding number (a) of closed circular DNA occur widely in nature (1-5). The topological winding number is the number of revolutions that one strand makes about the other if the molecule is constrained to lie in a plane. The activities have been demonstrated to be enzymatic with proteins from Escherichia coli (6), mouse (7), and human (8) cells in culture. The N-C enzyme from mouse LA9 cell nuclei, purified to homogeneity in good yield, is a major constituent of chromatin and accounts for about 1% of the total protein (H-P.Vosberg and J. Vinograd, unpublished work). It is similar to other eukaryotic N-C enzymes in its ability to relax both positive and negative superhelical turns. A probable in vivo role for the enzyme is to provide the transient swivels required for DNA replication. Such swivels may also be required in transcription, and in the condensation and decondensation of chromatin.In this study we have examined the limit product of the action of N-C enzyme on several closed circular DNAs by gel electrophoresis. Under appropriate analytical conditions, the limit product separates into a set of species differing in topological winding number. Individual species, isolated from the set, regenerate the original distribution upon incubation with the N-C enzyme. We view the foregoing as the consequence of four necessary events: nicking of the DNA, relaxation, random rotation about the swivel, and closure (Fig. 1). A set of species is also found when E. colh polynucleotide ligase is used to close a nicked circular DNA (9, 10). It is shown here that distribution of products obtained with ligase is indistinguishable from that obtained with N-C enzyme when the incubation conditions are the same for both reactions.The relative masses of the species, when plotted against a, fall on a Gaussian curve. Such a curve is anticipated for a Boltzmann distribution, when the energy of supercoiling is Abbreviations: N-C, nicking-closing; EtdBr, ethidium bromide.proportional to the square (11) of the degree of supercoiling. The similarity of the products obtained with two different enzyme systems and the further similarities of the values of the free energy of supercoiling obtained...