Polymer translocation through a nanopore - a showcase of anomalous diffusion

Abstract

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {\em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $\alpha =2/(2\nu +2-{\gamma }_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {\em fractional} diffusion equation which is solved exactly in the interval $0<s<N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $<s(t)>$, and $<s^2(t)>-<s(t){>}^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

5 pages, 3 figures, accepted for publication in Phys. Rev. E

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Cited by in corpus (38)

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• Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore
• Dynamical Scaling Exponents for Polymer Translocation through a Nanopore
• Comment on ``Passage Times for Unbiased Polymer Translocation through a Narrow Pore''
• Pore-blockade Times for Field-Driven Polymer Translocation
• Scaling exponents of Forced Polymer Translocation through a nano-pore
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
• Stochastic calculus for uncoupled continuous-time random walks
• Dynamics of forced biopolymer translocation
• Out of Equilibrium Characteristics of a Forced Translocating Chain through a Nanopore
• Anomalous Diffusion with Absorbing Boundary
• Fractional Brownian motion approach to polymer translocation: the governing equation of motion
• Through the Eye of the Needle: Recent Advances in Understanding Biopolymer Translocation
• Polymer Translocation out of Planar Confinements
• Polymer translocation into a fluidic channel through a nanopore
• Critical evaluation of the computational methods used in the forced polymer translocation
• Translocation Dynamics with Attractive Nanopore-Polymer Interactions
• Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions
• Polymer Translocation Dynamics in the Quasi-Static Limit
• Non-driven polymer translocation through a nanopore: computational evidence that the escape and relaxation processes are coupled
• Probability distributions for polymer translocation
• Dynamics of DNA translocation through an attractive nanopore
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• Simulations of Two-Dimensional Unbiased Polymer Translocation Using the Bond Fluctuation Model
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• Polymer translocation out of confined environments
• Driven polymer translocation through a cylindrical nanochannel: Interplay between the channel length and the chain length
• Polymer translocation into laterally unbounded confined environments
• Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics
• Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study
• Escape transition of a polymer chain from a nanotube: how to avoid spurious results by use of the force-biased pruned-enriched Rosenbluth algorithm
• Free Energy Evaluation in Polymer Translocation via Jarzynski Equality
• Response of Single Polymers to Localized Step Strains
• Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
• Markov Chain Modeling of Polymer Translocation Through Pores
• Finite-size scaling in unbiased translocation dynamics
• Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions