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Polymer translocation under time-dependent driving forces: Resonant activation induced by attractive polymer-pore interactions
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10.1063/1.4722080
/content/aip/journal/jcp/136/20/10.1063/1.4722080
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/20/10.1063/1.4722080
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A schematic representation of the system. The polymer, placed initially on the cis side, is driven through the pore of length L = 5 and width W = 3 by the time-dependent external force F + f(t).

Image of FIG. 2.
FIG. 2.

The mean translocation time τ and the probabilities P 0 and P τ (see text) as a function of the flipping rate ω of the dichotomic force for the repulsive pore. N = 64, F = 0.3, A d = 0.2, and τ0 ≈ 750 ± 4. The statistical error is smaller than the symbol size.

Image of FIG. 3.
FIG. 3.

Illustration of the free energy of the polymer chain as a function of the number of translocated monomers s. The dotted line indicates the free energy for the non-attractive pore, which has no well structure. A reflecting boundary condition at s = 0 forms a free-energy well (blue shaded area). Attractive polymer-pore interactions can also create a free-energy well (schematically shaded red).

Image of FIG. 4.
FIG. 4.

The distribution of translocation times for chain length N = 64 and F = 0.3 under dichotomic driving force in the non-attractive pore. Panel (a) shows the distribution for A d = 0, while panels (b)–(d) show the distribution for A d = 0.2.

Image of FIG. 5.
FIG. 5.

The mean translocation time τ and the probabilities P 0 and P τ as a function of the angular frequency ω for the periodic force and repulsive pore. N = 64, F = A = 0.3, and τ0 ≈ 750 ± 4. The statistical error is smaller than the symbol size.

Image of FIG. 6.
FIG. 6.

Comparison between LD simulations (N = 64, F = A = 0.3) and the theoretical toy model. Dotted line: toy model with uniformly distributed ϕ; solid line: toy model with Boltzmann distributed ϕ (see text). The latter shows good agreement with the LD results (circles).

Image of FIG. 7.
FIG. 7.

The distribution of translocation times for chain length N = 64 and F = 0.3 under sinusoidal driving force in the non-attractive pore. Panel (a) shows the distribution for A = 0, while panels (b)–(f) show the distribution for A = 0.3.

Image of FIG. 8.
FIG. 8.

The mean translocation time τ and the probabilities P 0 and P τ for the dichotomic force and attractive pore. N = 32, F = 0.5, A d = 0.2, εpm = 1, and τ0 ≈ 226.8 ± 0.6. The statistical error is smaller than the symbol size.

Image of FIG. 9.
FIG. 9.

The mean translocation time τ and the probabilities P 0 and P τ for the dichotomic force and attractive pore. N = 32, F = 0.5, A d = 0.2, εpm = 2.5, and τ0 ≈ 2202 ± 29. The statistical error is smaller than the symbol size.

Image of FIG. 10.
FIG. 10.

The translocation process divided into three stages: (1) initial filling of the pore, (2) transfer of the polymer from the cis side to the trans side, and (3) the final emptying of the pore. The corresponding times of the subprocesses are τ1, τ2, and τ3, with the total translocation time τ = τ1 + τ2 + τ3.

Image of FIG. 11.
FIG. 11.

The times τ1, 2 (dashed lines) and τ3 (solid lines) for εpm = 1 (squares) and εpm = 2.5 (circles). Here N = 32, F = 0.5, A d = 0.2 for both cases. While τ1, 2 monotonically decreases as ω increases, τ3 shows a resonant minimum. The statistical error is smaller than the symbol size.

Image of FIG. 12.
FIG. 12.

The distribution of translocation times for the dichotomic force and attractive pore. N = 32, F = 0.5, and A d = 0.2. The left column shows the distributions for εpm = 1 and the right column for εpm = 2.5.

Image of FIG. 13.
FIG. 13.

Translocation times for chain lengths 16 ⩽ N ⩽ 128 with the dichotomic force and attractive pore. F = 0.5, A d = 0.2, and εpm = 2.5. While the optimal rescaled flipping rate (ωτ0) shows a slight dependence on N (main figure), the unnormalized flipping rate (ω) is independent of N (inset). The statistical error is smaller than the symbol size.

Image of FIG. 14.
FIG. 14.

Translocation times for driving forces 0.5 ⩽ F ⩽ 4 for the dichotomic force and attractive pore. A d = 0.4F, εpm = 2.5. In this case, the optimal rescaled flipping rate (ωτ0) is roughly independent of F (main figure), while the unnormalized flipping rate (ω) strongly increases with F (inset). The statistical error is smaller than the symbol size.

Image of FIG. 15.
FIG. 15.

Translocation times for the dichotomic force and attractive pore for amplitudes A d ∈ {0.2, 0.4, 0.8, 1.6}. F = 0.5, εpm = 2.5. The statistical error is smaller than the symbol size.

Image of FIG. 16.
FIG. 16.

Translocation time τ as a function of frequency ω for the periodic driving force f(t) = Asin (ωt + ϕ) for 0.1 ⩽ εpm ⩽ 2.5. F = 0.5, A = 0.3, and N = 32. The inset shows a magnification of the data for 0.1 ⩽ εpm ⩽ 1.5. The statistical error is smaller than the symbol size.

Image of FIG. 17.
FIG. 17.

Translocation time τ as a function of frequency ω for the periodic driving force f(t) = Asin (ωt + ϕ) for amplitudes A ∈ {0.3, 0.6, 0.8, 1.0, 1.2, 1.5, 1.8, 2.4, 3.0}. Other parameters are F = 0.5, εpm = 2.0, and N = 32. The inset shows the dependence of the frequency ωmin of the global minimum translocation time on the amplitude A. Here τ0 ≈ 500 ± 6. The statistical error is smaller than the symbol size.

Image of FIG. 18.
FIG. 18.

The translocation time τ and its components τ1, 2 and τ3 as a function of ω, showing that the leftmost minimum in τ(ω) is associated with τ1, 2. Parameter values used are F = 0.5, A = 1.0, εpm = 2.0, and N = 32. The statistical error is smaller than the symbol size.

Image of FIG. 19.
FIG. 19.

Distribution of translocation times for the periodic driving force with N = 32, εpm = 2.0, F = 0.5, A = 0.0 (panel (a)), A = 1.0 (panels (b)–(f)).

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/content/aip/journal/jcp/136/20/10.1063/1.4722080
2012-05-31
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Polymer translocation under time-dependent driving forces: Resonant activation induced by attractive polymer-pore interactions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/20/10.1063/1.4722080
10.1063/1.4722080
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