The time evolution of the polymer configuration during the translocation process, with time advancing from left to right. The arc denotes the position of the tension front , which separates the chain into the moving and nonmoving domains. The last monomer inside the front is denoted by N and the number of translocated monomers by .
Comparison of waiting times w for MD (squares) and the BDTP model (circles). The agreement of the BDTP model with MD simulations is excellent, and reveals the two stages of translocation: the tension propagation stage of increasing and the tail retraction stage characterized by decreasing . For both MD and BDTP the data have been averaged over 2000 successful translocation events and the system parameters are the same (N 0 = 256, f = 5, k B T = 1.2, η = 0.7).
The waiting times per monomer as a function of monomer number . In the long chain length limit, , implying the scaling . Model parameters used are f = 5.0, k B T = 1.2, η = 0.7, ν = 0.588 (3D).
The exponent α ( ) as a function of driving force and chain length N 0. The position of the circle denotes the combination of and, the size reflects the value of α. Next to the symbols, the numerical values of α from the BDTP model are shown in comparison with the values from MD simulations written in parentheses. The asymptotic value of α is indicated in the upper right corner.
The effective exponent as a function of chain length N 0 for the BDTP model solved for driving forces f = 0.75, 1.5, 2.0, 3.0, 5.0, 10.0. Other parameters are k B T = 1.2, η = 0.7, η p = 5.0. Errors are of the order of the symbol size. Inset: α(N 0) for f = 3.0, 5.0, 10.0 up to N 0 = 1010, showing the approach to the asymptotic value α(N 0 → ∞) = 1 + ν.
The pore friction η p as a function of the pore diameter d. The symbols indicate the results obtained from MD simulations for different solvent frictions η, while the solid line is an empirical fitting function. The pore friction η p includes a non-vanishing contribution pη from the p monomers inside and in the immediate vicinity of the pore. For p, we find p ≈ 2.5, giving the total pore friction , where ηLJ is given by the choice of the Lennard-Jones units (see text). The chain length is N 0 = 100, with other parameters the same as in Fig. 3 .
The effective exponent α(N 0) averaged over different chain length regimes shown as a function of pore diameter d. Model parameters are the same as in Fig. 6 .
The effective exponent α(N 0) as a function of chain length N 0 for the BDTP model solved for different ratios of pore and solvent friction. Parameters used are the same as in Fig. 6 .
The dependence of τ on f measured from the BDTP model with N 0 = 128 and k B T = 1.2, γ = 0.7. The inset shows the exponent δ (τ ∼ f δ) as a function of f for both BDTP and MD. Here MD (1) corresponds to η = 0.7 and k = 15, MD (2) to η = 10 and k = 15, and MD (3) to η = 10 and k = 150. For δ, the error is of the order of the size of the symbols.
The translocation coordinate as a function of time for the BDTP model (filled symbols) and MD simulations (open symbols) for N 0 = 100. Other parameters are the same as in Fig. 3 . Inset: for η = 0.7 and η = 10, showing the difference between the inertial and overdamped regimes.
The exponent β ( , left panel) and the product of the exponents α and β (right panel) as a function of chain length. The dashed lines indicate the theoretical asymptotic values β(N 0 → ∞) = 1/(1 + ν) and αβ(N 0 → ∞) = 1. Model parameters are the same as in Fig. 10 .
The fluctuations of the translocation coordinate (left) and the distribution of translocation times (right) for the BDTP model and molecular dynamics simulations. In the BDTP model, the trans side subchain is not modeled, which reduces fluctuations.
The translocation coordinate as a function of time from MD simulations. The chain is either allowed to escape the pore to the cis side (open symbols, same data as in Fig. 10 ) or such an escape is prevented by a reflecting boundary condition (RBC, filled symbols). The results change drastically, if the RBC is used. Inset: the scaling exponent β ( ) as a function of the driving force f both without and with the RBC. Parameters are the same as in Fig. 10 .
(Left panel) Geometry of the pore used in the 3D MD simulations. The pore is formed by placing 16 monomers of diameter σ equidistantly on a circle of radius (d + σ)/2, resulting in a pore of diameter d. (Right panel) A side-view of the pore and the wall, also showing a typical initial configuration of the chain and the direction of the driving force f.
The velocity perpendicular to the wall of individual monomers for chain lengths N 0 = 100 (upper panel) and N 0 = 500 (lower panel) as a function of normalized perpendicular distance from the wall. The location of the tension front is given by . The different plots correspond to different instances in time, with the average ⟨·⟩ taken over 10 000 independent runs and a time window Δt = 1. The solid black line indicates the empirical fitting function of Eq. (B1) with b ≈ 1.9. In the BDTP model, the parameter b is not found by fitting, but fixed by global mass conservation. However, the resulting numerical value is comparable to the value found in MD simulations.
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