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

Abstract

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.

Model microswimmers in channels with varying cross section

“…Interestingly, it has been shown that for some cases [58] these generic far-field expansions quantitatively capture the hydrodynamic interactions with bounding walls even when the microswimmers are very close to these walls. As a result, hydrodynamic interactions between 6 The term "entropic" stems from the fact that h(x) − R measures the number of states available in the transverse direction and therefore ln[(h(x) − R)/d] is proportional to the local entropy. 7 The probability distribution in Eq.…”

“…In order to derive analytical expressions, we assume that the channel cross section varies smoothly enough such that swimmers explore the cross-sectional direction while moving along the channel axis. In such a regime, the Fick-Jacobs approximation [3,4,8,10,31,51,65] properly captures the overall dynamics of systems as diverse as molecular motors [37,39,42], driven particles [52,53], electrokinetic phenomena [40,43,44], and polymer translocation [6] just to mention a few among others (see recent review articles [7,24,38] for a more comprehensive list). Here, we extend the Fick-Jacobs approximation to active particles 1 and we will characterize the motion of microswimmers in narrow channels with corrugated walls.…”

Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness

“…Since bead-spring models form the basis of much contemporary theory for polymer glasses and their material properties, this finding has broad consequences across polymer physics. Indeed, nonmonotonicity of dynamic quantities with respect to chain length and stiffness is emerging as a widespread feature of polymeric systems in various contexts [28,29]. It is, so far, difficult to isolate bending stiffness experimentally, since many other factors can influence the mechanical properties.…”

Rectification and Non-Gaussian Diffusion in Heterogeneous Media

“…As a second case, we will analyze the motion of a Brownian particle moving in a confined medium which induces x-dependent entropic forces [15][16][17][18][19][20][21][22][23][24]. Such a situation is typically observed in molecules moving through ion-channels or membrane pores [25][26][27][28][29][30], and for molecular motors in porous media [31][32][33], to mention just a few among others.…”