Diffusion in an elastic medium: A model for macromolecule transport across the nuclear pore complex

Nuclear pore complexes (NPCs) are very selective filters that sit on the membrane of the nucleus and monitor the transport between the cytoplasm and the nucleoplasm. For the central plug of NPC two models have been suggested in the literature. The first suggests that the plug is a reversible hydrogel while the other suggests that it is a polymer brush. Here we propose a model for the transport of a protein through the plug, which is general enough to cover both the models. The protein stretches the plug and creates a local deformation, which together with the protein, we refer to as the bubble. We start with the free energy for creation of the bubble and consider its motion within the plug. The relevant coordinate is the center of the bubble which executes random walk. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. •An analytical theory for the transport of macromolecules through nuclear pore complex.•Valid for brush as well as gel picture of nuclear pore complex.•Enhancement of diffusion due to fluctuations in elastic environment.•Selectivity in protein transport arises as a result of the competition between elastic, deformation and contact energy.