Nucleocytoplasmic transport (NCT) is affected in several neurodegenerative diseases including C9orf72-ALS. It has recently been found that arginine-containing dipeptide repeat proteins (R-DPRs), translated from C9orf72 repeat expansions, directly bind to several importins. To gain insight into how this can affect nucleocytoplasmic transport, we use coarse-grained molecular dynamics simulations to study the molecular interaction of poly-PR, the most toxic DPR, with several Kapβs (importins and exportins). We show that poly-PR-Kapβ binding depends on the net charge per residue (NCPR) of the Kapβ, salt concentration of the solvent, and poly-PR length. Poly-PR makes contact with the inner surface of most importins, which strongly interferes with Kapβ binding to cargo-NLS, IBB, and RanGTP in a poly-PR length-dependent manner. Longer poly-PRs at higher concentrations are also able to make contact with the outer surface of importins that contain several binding sites to FG-Nups. We also show that poly-PR binds to exportins, especially at lower salt concentrations, interacting with several RanGTP and FG-Nup binding sites. Overall, our results suggest that poly-PR might cause length-dependent defects in cargo loading, cargo release, Kapβ transport and Ran gradient across the nuclear envelope.