The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluct
uations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.
During polymer translocation driven by e.g. voltage drop across a nanopore, the segments in the cis-side is incessantly pulled into the pore, which are then pushed out of it into the trans-side. This pulling and pushing polymer segments are described
in the continuum level by nonlinear transport processes known, respectively, as fast and slow diffusions. By matching solutions of both sides through the mass conservation across the pore, we provide a physical basis for the cis and trans dynamical asymmetry, a feature repeatedly reported in recent numerical simulations. We then predict how the total driving force is dynamically allocated between cis (pulling) and trans (pushing) sides, demonstrating that the trans-side event adds a finite-chain length effect to the dynamical scaling, which may become substantial for weak force and/or high pore friction cases.
Two phase picture is a simple and effective methodology to capture the nonequilibrium dynamics of polymer associated with tension propagation. When applying it to the driven translocation process, there is a point to be noted, as briefly discussed in
our recent article [Phys. Rev. E 85, 061803 (2012)]. In this article, we address this issue in detail and modify our previous prediction [Euro. Phys. J. E 34, 135 (2011)] by adopting an alternative steady-state ansatz. The modified scaling prediction turns out to be the same as that of the iso-flux model recently proposed by Rowghanian and Grosberg [J. Phys. Chem. B 115, 14127-14135 (2011)].
We discuss the temporal distribution of dynamic processes in driven polymer transport inherent to flexible chains due to stochastic tension propagation. The stochasticity originates from the disordered initial configuration of an equilibrium polymer
coil, which results in random paths for tension propagation. We consider the process time for when translocation occurs across a fixed pore and when stretching occurs by pulling the chain end. A scaling argument for the mean and standard deviation of the process time is provided using the two-phase picture for stochastic propagation. The two cases are found to differ remarkably. The process time distribution of the translocation exhibits substantial spreading even in the long-chain limit, unlike that found for the dynamics of polymer stretching. In addition, the process time distribution in the driven translocation is shown to have a characteristic asymmetric shape.
