Theory of capture rate in polymer translocation

The translocation of macromolecules through a nanopore requires the impingement of the molecules at the pore followed by threading through the pore. While most of the discussion on the translocation phenomenon focused so far on the threading process, the phenomenology on the frequency of encounters between the polymer and the pore exhibits diverse features in terms of polymer length, solution conditions, driving force, and pore geometry. We derive a general theory for the capture rate of polyelectrolyte molecules and the probability of successful translocation through a nanopore, under an externally imposed electric field. By considering the roles of entropic barrier at the pore entrance and drift of the polyelectrolyte under the electric field, we delineate two regimes: (a) entropic barrier regime and (b) drift regime. In the first regime dominated by the entropic barrier for the polyelectrolyte, the capture rate is an increasing nonlinear function in the electric field and chain length. In the drift regime, where the electric field dwarfs the role of entropic barriers, the capture rate is independent of chain length and linear in electric field. An analytical formula is derived for the crossover behavior between these regimes, and the general results are consistent with various experimentally observed trends.