The nuclear pore complex, the only pathway for transport between the nucleus and cytoplasm, functions as a highly selective gate that blocks nonspecific macromolecules while allowing the rapid transport of tagged [transport factor (TF) bound] cargo up to an order of magnitude larger. The mechanism of this gate's operation is not yet fully understood and progress has been primarily hindered by the inherent complexity and multiscale nature of the problem. One needs to consider the hundreds of disordered proteins (phenylalanine glycine nucleoporins or FG nups) lining the pore, as well as their overall architecture and dynamics at the microsecond scale, while also accounting for transport at the millisecond scale across the entire pore. Here we formulate an approach that addresses transport properties over a large range of length and time scales. We do this by incorporating microscopic biophysical details, such as charge and specific TF-FG nup interactions, to compute the free energy landscape encountered by the cargo. We connect this to macroscopic transport by treating cargo translocation as a stochastic barrier crossing process and computing the current and the translocation time. We then identify distinct transport regimes (fast permeable, slow permeable, and impermeable) determined by the cargo size, TF affinity for FG nups, and the activity of the enzymes that cleave TFs from cargo. Our results, therefore provide an integrated picture of transport through the NPC, while highlighting how FG nup interactions with TFs and enzyme activity cooperate to produce selectivity and efficiency.