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

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

2010-07-22

arxiv.org/abs/1007.3853v2

Phys. Rev. E, 83, 011802 (2011)

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 7 figures; Accepted for publication in Phys. Rev. E; Replacement of arXiv:1007.3853v1: 1) Added new references 2) Ch

Scientific paper

10.1103/PhysRevE.83.011802

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.

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