The major energy source for nuclear transport is:
Energy input driving selective accumulation of proteins inside nucleus does not come from kinesin ATP hydrolysis used for microtubule transport or proton motive force powering mitochondrial import, but from compartmentalized GTP turnover of Ran. RCC1 guanine exchange factor bound to nucleosomes continuously recharges Ran-GDP to Ran-GTP using nuclear GTP pool, while cytoplasmic RanGAP1 SUMOylated and anchored to RanBP2/Nup358 plus co-activator RanBP1 hydrolyze GTP outside. Each import cycle consumes one GTP upon export complex disassembly in cytosol, and each export cycle consumes GTP as Ran-GT
Ref: NCBI Bookshelf, Molecular Biology of the Cell, Section: GTP Hydrolysis by Ran as Energy Source.