This data is from BS3 crosslinked condensin tetramer How protein complexes of the SMC family fold DNA into the large loops that are fundamental for the 3D organization of genomes is a central unresolved question of chromosome biology. We used electron cryomicroscopy to investigate the reaction cycle of the SMC complex condensin, which is a key determinant of chromosome morphology and behavior during mitosis. Our structures of the Saccharomyces cerevisiae condensin holo complex at different functional stages suggest that ATP binding induces the transition from a folded-rod SMC conformation into an open architecture and triggers the exchange of the two HEAT-repeat subunits at the SMC ATPase head domains. We propose that these steps result in the interconversion of DNA binding sites in the catalytic core that form the basis of the DNA translocation and loop-extrusion activities of condensin.