Anomalous dynamics of forced translocation

Abstract

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N 2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (sub-diffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N 2 and N 1+ν , respectively, where ν is the exponent that relates the scaling of the radius of gyration to N . Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N = 512).

Nonequilibrium dynamics of polymer translocation and straightening

“…(21). It is in this limit only that the requirement τ ∼ f −1 is fulfilled reflecting the saturation of chain deformation due to the complete stretching, therefore, the earlier conjectures are approved [8,11]. For smaller forces, the soft elasticity of the chain results in more involved responses as we have seen; the stronger driving results in the more intense chain deformation, and this deformation behaviour affects the absorption dynamics.…”

“…For a chain with excluded volume studied by Kantor and Karder, a similar scaling argument leads to [8] …”

“…Our target here is the dynamical process, in which a polymer is sucked into a localized hole. This is different from the pulling the chain's one end [8], but similar in the way how the chain responds to the local force, and, in fact, relevant to the dynamics of polymer translocation through hole [9,10] and the adsorption process to a small particle. (In this case, the force f is related to the chemical potential change ∆µ due to the absorption via f = ∆µ/b.)…”

“…Although the phenomenon of polymer translocation has been an active research topic in the past decade as a model for biopolymer transport through a pore in membrane, our current understanding for the dynamics, in particular the strongly driven case, is restrictive. So far, the scaling estimates of the characteristic time τ for absorption process in immobile solvents have been proposed [8,11]. Grosberg et.…”

Direct observation of DNA knots using a solid-state nanopore

“…For long polymers, the translocation process is much faster than the typical relaxation time 29 , which allows us to investigate the polymers before they have a chance to relax. This enables us to probe long DNA molecules for the presence of topological structures such as knots.…”