Dynamical diagram and scaling in polymer driven translocation

Saito, Takuya; Sakaue, Takahiro

doi:10.1140/epje/i2011-11135-3

Cited by 77 publications

(144 citation statements)

References 28 publications

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“…Using blob theory, it is possible to describe the shape of the mobile part and the propagation of the boundary between the mobile and immobile parts self-consistently. [18][19][20][21][22][23][24][25][26][27] Asymptotic analysis of this tension propagation theory also gives the long chain limit of the translocation time as τ = c 1 N 1+ν 0 , similar to the simple scaling arguments. 28 Numerical analysis has shown that the finite chain length effects due to the pore friction persist for extremely long chains, and that they are responsible for the scatter in the reported values of the scaling exponent α.…”

Section: Introductionmentioning

confidence: 92%

Iso-flux tension propagation theory of driven polymer translocation: The role of initial configurations

Sarabadani

Ikonen

Ala-Nissilä

2014

The Journal of Chemical Physics

130

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We investigate the dynamics of pore-driven polymer translocation by theoretical analysis and molecular dynamics (MD) simulations. Using the tension propagation theory within the constant flux approximation we derive an explicit equation of motion for the tension front. From this we derive a scaling relation for the average translocation time τ , which captures the asymptotic result τ ∝ N 1+ν 0 , where N0 is the chain length and ν is the Flory exponent. In addition, we derive the leading correction-to-scaling term to τ and show that all terms of order N 2ν 0

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Section: Introductionmentioning

confidence: 92%

Iso-flux tension propagation theory of driven polymer translocation: The role of initial configurations

Sarabadani

Ikonen

Ala-Nissilä

2014

The Journal of Chemical Physics

130

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“…[5] for a recent review). Several theories of driven polymer translocation have emerged [6][7][8][9][10][11][12][13][14][15][16], some claiming agreement with the experimental or numerical results within a certain subset of the physical parameter space. However, to date no single theory has been able to capture the wide range of observed values of α, nor quantitatively explain the reason for their dependence on the system's parameters.…”

Section: Introductionmentioning

confidence: 97%

Unifying model of driven polymer translocation

et al. 2012

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We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by solving the model for chain lengths up to 10 10 monomers, we show that the chain lengths probed by experiments and simulations are typically orders of magnitude below the asymptotic limit. This explains both the considerable scatter in the observed scaling of translocation time with respect to chain length, and some of the shortcomings of present theories. Our study shows that for a quantitative theory of polymer translocation, explicit consideration of finite chain length effects is required.

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“…This scenario has been treated within the linear response theory (that is, for relatively weak driving forces) and the corresponding memory function has been derived explicitly [7,8]. For arbitrary strong driving forces, an interesting approach based on the notion of tensile force propagation along the chain backbone has been suggested by Sakaue [9][10][11]. Sakaue's idea has been used and worked out very recently in other theoretical treatments [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…It is important to determine the origin of this inconsistency since apparently there is something missing in the aforementioned theoretical consideration which gives room for speculations. For example, in a paper by Ikonen et al [12], the model based on the idea of tensile force propagation [9][10][11] and the role of pore-polymer friction has been numerically investigated. The authors argue that the theoretical value for the exponent, α = 1 + ν, may be seen only for very long chains whereas for the chain lengths used in real experiments or simulations the effective exponent α could be approximately 20% smaller.…”

Section: Introductionmentioning

confidence: 99%

Driven translocation of a polymer: Fluctuations at work

et al. 2013

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The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive molecular dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, s (t), that have passed through the pore at time t due to a driving force f . The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity v =ṡ(t) is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a time-dependent diffusion coefficient D(t). Our MD simulation reveals that the driven translocation process follows a super diffusive law with a running diffusion coefficient D(t) ∝ t γ where γ < 1. This finding is then used in the numerical solution of the FPE which yields an important result: For comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent α which describes the scaling of the mean translocation time τ with the length N of the polymer, τ ∝ N α is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the nondriven case, f = 0, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).

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Dynamical diagram and scaling in polymer driven translocation

Cited by 77 publications

References 28 publications

Iso-flux tension propagation theory of driven polymer translocation: The role of initial configurations

Iso-flux tension propagation theory of driven polymer translocation: The role of initial configurations

Unifying model of driven polymer translocation

Driven translocation of a polymer: Fluctuations at work

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