Translocation of polymers in a lattice model.

Voltage-driven polymer translocation is studied by means of a stochastic lattice model. The model incorporates voltage drop over the membrane as a bias in the hopping rate through the pore and exhibits the two main ingredients of the translocation process: driven motion through the pore and diffusive supply of chain length towards the pore on the cis-side and the drift away from the pore on the trans-side. The translocation time is either bias limited or diffusion limited. In the bias-limited regime the translocation time is inversely proportional to the voltage drop over the membrane. In the diffusion-limited regime the translocation time is independent of the applied voltage, but it is rather sensitive to the motion rules of the model. We find that the whole regime is well described by a single curve determined by the initial slope and the saturation value. The dependence of these parameters on the length of the chain, the motion rules and the repton statistics are established. Repulsion of reptons as well as the increase of chain length decrease the throughput of the polymer through the pore. As for free polymers, the inclusion of a mechanism for hernia creations/annihilations leads to the cross-over from Rouse-like behaviour to reptation. For the experimentally most relevant case (Rouse dynamics) the bimodal power law dependence of the translocation time on the chain length is found.