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Assemblies of structural maintenance of chromosomes (SMC) proteins and kleisin subunits are essential to chromosome organization and segregation across all kingdoms of life. While structural data exist for parts of the SMC−kleisin complexes, complete structures of the entire complexes have yet to be determined, making mechanistic studies difficult. Using an integrative approach that combines crystallographic structural information about the globular subdomains, along with coevolutionary information and an energy landscape optimized force field (AWSEM), we predict atomic-scale structures for several tripartite SMC−kleisin complexes, including prokaryotic condensin, eukaryotic cohesin, and eukaryotic condensin. The molecular dynamics simulations of the SMC−kleisin protein complexes suggest that these complexes exist as a broad conformational ensemble that is made up of different topological isomers. The simulations suggest a critical role for the SMC coiled-coil regions, where the coils intertwine with various linking numbers. The twist and writhe of these braided coils are coupled with the motion of the SMC head domains, suggesting that the complexes may function as topological motors. Opening, closing, and translation along the DNA of the SMC−kleisin protein complexes would allow these motors to couple to the topology of DNA when DNA is entwined with the braided coils.