Previous studies suggest that the global secondary structures of native supercoiled and equilibrium linear DNAs may differ somewhat. Recent evidence also indicates that metastable secondary structure commonly persists following complete relaxation of the superhelical stress by intercalating dyes or by the action of topoisomerase I. In this work, the torsion constants (alpha) of pBR322, pUC8 and M13mp7 (replicative form) DNAs are determined by time-resolved fluorescence polarization anisotropy at various times subsequent to linearization. In all three cases, the torsion constants are relatively low immediately after linearization, and evolve for eight to ten weeks before reaching their apparent equilibrium values. It is shown in detail how the persistence of metastable secondary structure, subsequent to relaxation of superhelical stress, necessarily implies that one or more transitions in equilibrium secondary structure are induced as the superhelix density is varied from zero to native, or vice versa. Samples of pUC8 dimer (5434 base-pairs) with different superhelix densities are prepared by the action of topoisomerase I in the presence of various amounts of ethidium. Their median linking number differences are determined by standard band counting methods. The translational diffusion coefficient (Do) and the plateau diffusion coefficient (Dplat) characterizing internal motions over short distances (225 A) are determined by dynamic light-scattering. The torsion constant (alpha) between base-pairs and the circular dichroism spectrum are also measured for each sample. Curves of Dplat, Do, alpha and molar ellipticity ([theta]) (at the minimum near 250 nm) versus superhelix density (sigma) are constructed. The curve of Do versus sigma is very similar to that for sedimentation coefficient versus sigma for simian virus 40 (SV40) and polyoma DNAs. The curves of Dplat, Do, alpha and [theta] versus sigma show that, with increasing negative superhelix density, a structural transition occurs near sigma = -0.020 to an intermediate state with low torsion constant, and a second structural transition occurs near sigma = -0.035 to a state that exhibits more normal properties by sigma = -0.048. These data are consistent with the hypothesis that supercoiling induces two successive allosteric transitions to alternative global secondary structures. The data are much less consistent with the hypothesis that supercoiling induces some radical secondary structure at one or a few sites of small extent at sigma = -0.020, and at other sites at sigma = -0.035, or with hypotheses based on changes in tertiary structure alone.(ABSTRACT TRUNCATED AT 400 WORDS)