Non-monotonous polymer translocation time across corrugated channels: comparison between Fick-Jacobs approximation and numerical simulations

We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like particle under the action of an effective potential. Such a model allows us to identify the relevant parameters controlling the polymers dynamics and, in particular, their translocation time. By comparing our analytical results with numerical simulations we show that, under suitable conditions, our model provides reliable predictions of the dynamics of both Gaussian and self-avoiding polymers, in two- and three-dimensional confinement. Moreover, both theoretical predictions, as well Brownian dynamic results, show a non-monotonous dependence of polymer translocation velocity as a function of polymer size, a feature that can be exploited for polymer separation.