Fractional Brownian motion approach to polymer translocation: the governing equation of motion

Abstract

We suggest a governing equation which describes the process of polymer chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time $t$ after the process has begun, and (ii) a sub-diffusive increase of the distribution variance $\Delta (t)$ with elapsed time, $\Delta (t)\propto t^{\alpha }$. The latter quantity measures the mean-squared number $s$ of polymer segments which have passed through the pore, $\Delta (t)=<[s(t)-s(t=0){]}^2>$, and is known to grow with an anomalous diffusion exponent $\alpha <1$. Our main assumption - a Gaussian distribution of the translocation velocity $v(t)$ - and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation which we performed in $3D$. We also numerically confirm the predictions made in ref.\cite{Kantor_3}, that the exponent $\alpha$ changes from $0.91$ to $0.55$, to $0.91$, for short, intermediate and long time regimes, respectively.

arXiv comment11 pages, 7 figures; Accepted for publication in Phys. Rev. E; Replacement of arXiv:1007.3853v1: 1) Added new references 2) Changed title 3) Improved figures

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• Polymer Translocation Dynamics in the Quasi-Static Limit
• The Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory
• Perturbative Expansion for the Maximum of Fractional Brownian Motion
• Fractional Brownian motion and the critical dynamics of zipping polymers
• Driven translocation of a polymer: fluctuations at work
• First passage in an interval for fractional Brownian motion
• Geometrical optics of large deviations of fractional Brownian motion
• The influence of absorbing boundary conditions on the transition path times statistics
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• Variational inference of fractional Brownian motion with linear computational complexity
• Path integrals for fractional Brownian motion and fractional Gaussian noise
• Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature
• First-passage area distribution and optimal fluctuations of fractional Brownian motion
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• Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves
• Observation time dependent mean first passage time of diffusion and sub-diffusion processes
• Markov Chain Modeling of Polymer Translocation Through Pores
• Functionals of fractional Brownian motion and the three arcsine laws