The (1-->3)-beta-D-glucans (scleroglucan, schizophyllan, lentinan, etc.) are of interest for their immunostimulatory activity. The native polymer dissolves in water as very stiff and stable triple-stranded helices, which can be dissociated to single strand random coils by heating to 135 degrees C. When the single-stranded material is returned to temperatures favoring formation of the triple helix, various structures are formed depending on polymer concentration and thermal history. With suitable annealing at sufficiently low polymer concentration, much of the renatured material appears as macrocycles with diameters that can reach several tens of nanometers; under the same conditions, the remaining material adopts a stiff linear molecular architecture that strongly resembles the linear triple helical starting material. The relative numbers of linear and cyclic species and the respective distributions of contour lengths and thicknesses were measured as a function of the annealing temperature using noncontact atomic force microscopy, The ratio of cyclic to linear species declines from about 2 to 0.5 as the annealing temperature rises from 70 to 130 degrees C. The mean lengths and thicknesses of both species are essentially constant over the same temperature range, but both the mean contour length and mean thickness are greater for the linear than for the cyclic species. These results are interpreted qualitatively in terms of a model for the renatured material that recognizes in the multistranded cyclic species a free energetic advantage arising from a structural degeneracy lacking in the linear forms. This degeneracy compensates effectively for the energetic and entropic barriers to cycle formation in the multistranded aggregates.