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Register a new userForced translocation of a polymer: dynamical scaling vs. MD-simulation
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Added by
Vakhtang Rostiashvili
Publication date
2011
fields
Physics
and research's language is
English
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We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of propagating front of tensile force along the chain backbone, suggested recently by T. Sakaue. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation, trumpet, stem-trumpet, etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasi-static approximation), we derive an equation of motion for the tensile front position $X(t)$. We show that the scaling law for the average translocation time $<tau>$ changes from $<tau> sim N^{2 u}/f^{1/ u}$ to $<tau> sim N^{1+ u}/f$ (for the free-draining case) as the dimensionless force ${widetilde f}_{R} = a N^{ u}f /T$ (where $a$, $N$, $ u$, $f$, $T$ are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by Molecular Dynamics (MD) simulation. Data from our computer experiment indicates indeed that the translocation scaling exponent $alpha$ grows with the pulling force ${widetilde f}_{R}$) albeit the observed exponent $alpha$ stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations which are neglected in the quasi-static approximation.
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We investigate several scaling properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulation in three dimension (3D). Specifically motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we determine the chain length dependence of the scaling exponents of the average translocation time, the average velocity of the center of mass, $<v_{CM}>$, the effective radius of gyration during the translocation process, and the scaling exponent of the translocation coordinate ($s$-coordinate) as a function of the translocation time. We further discuss the possibility that in the case of driven translocation the finite pore size and its geometry could be responsible that the veclocity scaling exponent is less than unity and discuss the dependence of the scaling exponents on the pore geometry for the range of $N$ studied here.
We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time $tau sim N^{alpha}$ and the mean-square change of the PT coordinate $<s^2(t)> sim t^beta$. We find $alpha=1+2 u$ and $beta=2/alpha$ for unbiased PT in 2D and 3D. The relation $alpha beta=2$ holds for driven PT in 2D, with crossover from $alpha approx 2 u$ for short chains to $alpha approx 1+ u$ for long chains. This crossover is, however, absent in 3D where $alpha = 1.42 pm 0.01$ and $alpha beta approx 2.2$ for $N approx 40-800$.
We present a theoretical argument to derive a scaling law between the mean translocation time $tau$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {it et al.}, Phys. Rev. E {bf 85}, 051803 (2012)] and molecular dynamics simulations that the rescaled exponent reaches the asymptotic limit in a range of chain lengths that is easily accessible to simulations and experiments. The rescaling procedure can also be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we also consider the case of driven translocation with hydrodynamic interactions (HIs). We show that by augmenting the BDTP theory with HIs one reaches a good agreement between the theory and previous simulation results found in the literature. Our results suggest that the scaling relation between $tau$ and $N$ is retained even in this case.
We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the {it cis} side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.
During polymer translocation driven by e.g. voltage drop across a nanopore, the segments in the cis-side is incessantly pulled into the pore, which are then pushed out of it into the trans-side. This pulling and pushing polymer segments are described in the continuum level by nonlinear transport processes known, respectively, as fast and slow diffusions. By matching solutions of both sides through the mass conservation across the pore, we provide a physical basis for the cis and trans dynamical asymmetry, a feature repeatedly reported in recent numerical simulations. We then predict how the total driving force is dynamically allocated between cis (pulling) and trans (pushing) sides, demonstrating that the trans-side event adds a finite-chain length effect to the dynamical scaling, which may become substantial for weak force and/or high pore friction cases.
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