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Using an incremental mean first passage approach to explore the viscosity dependent dynamics of the unbiased translocation of a polymer through a nanopore
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10.1063/1.4711865
/content/aip/journal/jcp/136/20/10.1063/1.4711865
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/20/10.1063/1.4711865

Figures

Image of FIG. 1.
FIG. 1.

Schematic of translocation. s represents the translocation coordinate by the number of monomers translocated to the right hand side. The translocation time τ is defined by the time required for the polymer to move from half-way s 0 = N/2 to either s = 0 or s = N. Although this image is in 2D for clarity, all simulations are done in 3D.

Image of FIG. 2.
FIG. 2.

α exponent derived from power law fits τ ∼ N α at different viscosities .

Image of FIG. 3.
FIG. 3.

The β exponent value derived from ⟨Δs(t)2⟩ ∼ t β for four polymer lengths at the selected viscosities: = 0.1, = 1.0, = 5.0.

Image of FIG. 4.
FIG. 4.

Sample translocation trajectories for N = 25 at given by s(t) plotted with t along the vertical axis. The shortest and longest trajectories (labelled) are shown along with eight other trajectories selected from an ensemble of 1000 events. The mean time along with the standard deviation of the mean (shaded region) are also indicated. The spread of this select set is indicative of the full ensemble distribution with the difference between the longest trajectory and the shortest trajectory being much larger than the mean.

Image of FIG. 5.
FIG. 5.

Normalized probability density function as a function of s for times t = 50, 100, 500, 1000, and 2000 at N = 49 and = 0.1. Approximate Gaussian fits are shown as dashed black lines. For early times (t = 50 and t = 100), the curves closely match a Gaussian curve with a width increasing as time progresses. Once translocation events begin occurring, data are only available for trajectories in which translocation has not yet occurred and the curves appear to collapse to a single curve with a constant width.

Image of FIG. 6.
FIG. 6.

Mean square displacement of the translocation coordinate versus time for = 0.1 and N = 25.

Image of FIG. 7.
FIG. 7.

Schematic representing the process of converting s(t) into t 0s).

Image of FIG. 8.
FIG. 8.

Average initial time t 0 to displacement Δs at a viscosity of for polymer lengths ranging from N = 25 to N = 299. The top set of curves display data from LD simulations. The bottom set of curves correspond to the equivalent data for the same polymer lengths as generated from using the exact methodology to solve the 1D model of translocation.

Image of FIG. 9.
FIG. 9.

Average time ⟨t 0⟩ to displacement Δs at a viscosity of for polymer lengths ranging from N = 25 to N = 149.

Image of FIG. 10.
FIG. 10.

Average initial time ⟨t 0⟩ to displacement |Δs| at a viscosity of for polymers lengths ranging from N = 25 to N = 299.

Image of FIG. 11.
FIG. 11.

Brownian dynamics results for the average time ⟨t 0⟩ to displacement Δs at a viscosity of for the polymer lengths N = 25,49,75,99.

Image of FIG. 12.
FIG. 12.

Normalized probability density function as a function of s for times t = 50, 100, 500, 1000, and 2000 at N = 49 and = 0.1. The forms predicted from Eq. (A2) are shown as black dashed lines.

Image of FIG. 13.
FIG. 13.

Analytic solution for the normalized peak height and probability of being absorbed plotted as a function of time for a = 24 and D = 0.25.

Image of FIG. 14.
FIG. 14.

Analytic solution at a = 24 and D = 0.25 and LD simulation results at N = 49 and for the normalized peak height and probability of being absorbed plotted as a function of time.

Image of FIG. 15.
FIG. 15.

Analytic solution at a = 24 and D = 0.05 and LD simulation results at N = 49 and for the normalized peak height and probability of being absorbed plotted as a function of time.

Tables

Generic image for table
Table I.

α and β exponents at the three selected viscosity values.

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/content/aip/journal/jcp/136/20/10.1063/1.4711865
2012-05-24
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Using an incremental mean first passage approach to explore the viscosity dependent dynamics of the unbiased translocation of a polymer through a nanopore
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/20/10.1063/1.4711865
10.1063/1.4711865
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