Recent cryo-electron microscopy (cryo-EM) results suggest that sufficient NaCl concentration (> or approximately 0.1 M) and superhelix density (> or approximately-0.05) cause circular DNAs to adopt highly extended, tightly interwound configurations, in which the strands are laterally contiguous along almost their entire length. Millimolar levels of MgCl2 reportedly act synergistically with NaCl to produce similar conformations. However, Monte Carlo simulations with purely repulsive interduplex forces failed to reproduce such structures. In the present work, solution measurements of particular physical properties were performed both to characterize the effects of Na+ and Mg2+ on DNA structure and to provide quantitative tests of Monte Carlo simulations of circular DNAs. Supercoiled p30 delta DNAs in 10 mM Tris plus 0, 0.122, and 0.1 M NaCl, and 0.1 M NaCl plus 4 mM Mg2+ were examined by static and dynamic light scattering (LS and DLS), time-resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium, and circular dichroism (CD) spectroscopy. Upon addition of 0.122 M NaCl, the radius of gyration (Rg) decreased substantially, which indicates that p30 delta adopts a more compact structure. This contradicts the cryo-EM studies, where molecular extension and Rg both increase upon adding 0.1 M NaCl. In 0.1 M NaCl, the torsion constant measured by FPA is practically invariant to superhelix density, and the plateau diffusion coefficient at large scattering vector (Dplat) is likewise nearly the same at both relaxed and native superhelix densities. Such invariance is difficult to reconcile with any transition from relaxed circles to tightly interwound structures with laterally contiguous strands. Metropolis Monte Carlo simulations were performed to generate canonically distributed sets of structures, from which average Do values and scattered intensity ratios, [symbol: see text]I (zero) [symbol: see text]/[symbol: see text] l(k) [symbol: see text], were calculated. Agreement between simulations and experiments in regard to [symbol: see text] I(O) [symbol: see text] /[symbol: see text] I(k) [symbol: see text], D(zero) and the supercoiling free energy, delta Gsc (delta l), is remarkably good for the most extensively studied p30 delta samples. The simulated structures exhibit no sign of very tight interwinding with extensive lateral contacts, but instead exhibit most probable superhelix diameters of 85 to 90 A. When 4 mM Mg2+ was added to native supercoiled p30 delta in 0.1 M NaCl, Rg decreased, D(zero) increased, and the longest internal relaxation rate (1/tau 2(zero)) increased, all of which indicate a further overall contraction of the molecular envelope. The torsion constant exhibited a slight increase that is hardly statistically significant. In this case, agreement between the simulations and experiments was only semi-quantitative for most samples investigated, although the predicted contraction was exhibited by all five samples of p30 delta and one of pBR322 DNA. The simulated structures in 0.1 M NaCl plus 4 mM Mg2+ again showed no sign of extensive lateral contacts. A plausible explanation is proposed for the highly extended, tightly interwound structures seen in cryo-EM, and explicitly tested by Monte Carlo simulations of a 1000 bp circular DNA at +25 and -50 degrees C. Structures identical to those seen in cryo-EM are in fact the equilibrium structures in the simulations at -50 degrees C, and the estimated time for equilibration (2.3 x 10(-6) second) is much smaller than the estimated time for vitrification (1 x 10(-4) second).