A mechanism of noncooperative (isodesmic) assembly coupled with preferential cyclization of long polymers is proposed to explain the previously posed question of how a single-stranded filament of the bacterial cell-division protein FtsZ can assemble in an apparently cooperative manner. This proposal is based on results of GTP-mediated assembly of FtsZ from Escherichia coli that was studied under physiologically relevant steady-state solution conditions by a combination of methods including measurement of sedimentation velocity, atomic force and electron microscopy, and precipitation assays. Sedimentation-velocity experiments carried out at multiple protein concentrations reveal an essentially bimodal distribution of slowly sedimenting species and a relatively narrow distribution of rapidly sedimenting species that appears only above an apparent "critical concentration" of protein. In a precipitation assay, the amount of protein that pellets, which correlates with the fraction of rapidly sedimenting species observed in sedimentation-velocity experiments, increases linearly with the total concentration of protein in excess of the critical concentration. Sedimentation coefficients of the rapidly sedimenting fraction are qualitatively consistent with the presence of single-stranded cyclic oligomers with a size range of approximately 50-150 protomers, similar to polymeric single-stranded rings observed in atomic force and electron micrographs. The proposed model is in accord with the results obtained from our experimental observations.