The ß-karyopherin/RanGTP system constitutes the largest known family of cellular cargo transporters. The flexibility of the karyopherin transport receptors is the key to their versatility in binding cargoes of different shape and size. Despite strong binding of the Ran complex, the comparably low energy associated with GTP hydrolysis suffices to drive dissociation and fuel the transport cycle. Here, we elucidate the drastic structural dynamics of the prototypic karyopherin, importin-ß, and show that its flexibility also solves this energetic puzzle. Our nonequilibrium atomistic simulations reveal fast conformational changes, validated by small-angle X-ray scattering data, and unusually large structural fluctuations. The characteristic dynamic patterns of importin-ß and the observed unfolding pathway of the IBB domain suggest a cooperative mechanism of importin-ß function in the nucleus. We propose a molecular model in which the stored energy and structural dynamics account for an exchange pathway that explains the high observed rates of nucleocytoplasmic transport. Karyopherins utilize a mechanism of entropy/enthalpy control that might be a general feature of highly flexible proteins involved in protein-protein interactions.