In biological systems, polymeric materials block the movement of some macromolecules while allowing the selective passage of others. We developed a model motivated by features of the nuclear pore complex (NPC) which are highly conserved and could potentially be applied to other biological systems. We show that a single feature of the NPC is sufficient for selective transport: the bound-state motion resulting from transient binding to flexible filaments. We generalized this observation to model nanoparticle transport through mucus as well. Our model provides a framework to control binding- induced selective transport in biopolymeric materials.