  Protein chains of the (FG)$_n$ ($n \simeq$ 300) type cap the cytoplasmatic
side of the nucleopore complex, which connects the nucleus to the remainder of
an eukaryotic cell. We study the properties of three fundamental polymer models
that represent these filaments using Monte Carlo computer simulations. Random
walks and the worm like chain model cannot account for the unusual size
selectivity of the pore, while a two-dimensional arrangement of intrinsically
disordered block copolymers with a high content of $\alpha$-helices is in
agreement with the biochemical findings. We predict a linear increase of the
free energy barrier of protein transport through the pore with increasing
protein diameter, which can be probed experimentally using atomic force
microscopy or optical tweezers.
