Polymer translocation through nanopores: Parking lot problems, scaling laws and their breakdown

. The passage of a polymer through a narrow pore is associated with the crossing of a significant free energy barrier. Both in nature and in single molecule experiments the polymer is typically driven through the pore. We here address two such driving modes: (i) the driving by binding proteins that prevent (partial) back-sliding through the pore; and (ii) the driving by a trans-membrane force. In case (i) we derive the effective force and show finite size effects due to the size of the binding proteins. In case (ii) we demonstrate the crossover from a slow, equilibrium driving to a non-equilibrium behaviour at fast driving.