Driven translocation of a polymer: fluctuations at work

Abstract

The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive Molecular-Dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, $s(t)$, that have passed through the pore at time $t$ due to a driving force $f$. The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity $v=\dot{s}(t)$ is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a {\em time-dependent} diffusion coefficient $D(t)$. Our MD simulation reveals that the driven translocation process follows a {\em super}diffusive law with a running diffusion coefficient $D(t)\propto t^{\gamma }$ where $\gamma <1$. This finding is then used in the numerical solution of the FPE which yields an important result: for comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent $\alpha$ which describes the scaling of the mean translocation time $<\tau >$ with the length $N$ of the polymer, $<\tau >\propto N^{\alpha }$ is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the non-driven case, $f=0$, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).

13 pages, 8 figures

References in corpus (9)

• Physical approaches to DNA sequencing and detection
• Nonequilibrium dynamics of polymer translocation and straightening
• Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion
• Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore
• Pore-blockade Times for Field-Driven Polymer Translocation
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
• Dynamics of forced biopolymer translocation
• Fractional Brownian motion approach to polymer translocation: the governing equation of motion
• Critical evaluation of the computational methods used in the forced polymer translocation

Cited by in corpus (13)

• Iso-Flux Tension Propagation Theory of Driven Polymer Translocation: The Role of Initial Configurations
• Theory of pore-driven and end-pulled polymer translocation dynamics through a nanopore: An overview
• Disentangling sources of anomalous diffusion
• Role of Non-Equilibrium Conformations on Driven Polymer Translocation
• Dynamics of driven translocation of semiflexible polymers
• Dynamics of end-pulled polymer translocation through a nanopore
• Using a Péclet Number for the Translocation of Polymer through a Nanopore to Tune Coarse-Grained Simulations to Experimental Conditions
• Chaperone-assisted translocation of flexible polymers in three dimensions
• Criteria for minimal model of driven polymer translocation
• Quantification of tension to explain bias dependence of driven polymer translocation dynamics
• Dynamics of polymer ejection from capsid
• Driven polymer translocation in good and bad solvent: effects of hydrodynamics and tension propagation
• Reducing the variance in the translocation times by pre-stretching the polymer