Translocation dynamics of a semiflexible chain under a bias: Comparison with tension propagation theory

Abstract

We study translocation dynamics of a semi-flexible polymer through a nanoscopic pore in two dimensions (2D) using Langevin dynamics simulation in presence of an external force inside the pore. We observe that for a given chain length N the mean first passage time (MFPT)〈τ〉 increases for a stiffer chain. By repeating the calculation for various chain lengths N and bending rigidity parameter κb we calculate the translocation exponent α (〈τ〉 ∼ Nα). For chain lengths N and bending rigidity κb considered in this paper we find that the translocation exponent satisfies the inequality α < 1 + ν, where is the equilibrium Flory exponent for a given chain stiffness, as previously observed in various simulation studies for fully flexible chains. We observe that the peak position of the residence time W(s) as a function of the monomer index s shifts at a lower s-value with increasing chain stiffness κb. We also monitor segmental gyration 〈Rg(s)〉 both at the cis and trans side during the translocation process and find that for κb ≠ 0 the late time cis conformations are nearly identical to the early time trans conformations, and this overlap continues to increase for stiffer chains. Finally, we try to rationalize dependence of various quantities on chain stiffness κb using Sakaue’s tension propagation (TP) theory [Phys. Rev. E 76, 021803 (2007)] and Brownian Dynamics Tension Propagation (BDTP) theory due to Ikonen et al. [Phys. Rev. E 85 051803 (2012); J. Chem. Phys. 137 085101 (2012)] originally developed for a fully flexible chain to a semi-flexible chain.