Molecular machines order and disorder polypeptides as they form and dissolve large intermolecular interfaces, but the biological significance of coupled ordering and binding has been established in few, if any, macromolecular systems. The ordering and binding of GroES co-chaperonin mobile loops accompany an ATP-dependent conformational change in the GroEL chaperonin that promotes client protein folding. Following ATP hydrolysis, disordering of the mobile loops accompanies co-chaperonin dissociation, reversal of the GroEL conformational change, and release of the client protein. "High-affinity" GroEL mutants were identified by their compatibility with "low-affinity" co-chaperonin mutants and incompatibility with high-affinity co-chaperonin mutants. Analysis of binding kinetics using the intrinsic fluorescence of tryptophan-containing co-chaperonin variants revealed that excessive affinity causes the chaperonin to stall in a conformation that forms in the presence of ATP. Destabilizing the beta-hairpins formed by the mobile loops restores the normal rate of dissociation. Thus, the free energy of mobile-loop ordering and disordering acts like the inertia of an engine's flywheel by modulating the speed of chaperonin conformational changes.