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Register a new userScaling exponents of Forced Polymer Translocation through a nano-pore
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Added by
Aniket Bhattacharya
Publication date
2008
fields
Physics
and research's language is
English
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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.
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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 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.
One of the most fundamental quantities associated with polymer translocation through a nanopore is the translocation time $tau$ and its dependence on the chain length $N$. Our simulation results based on both the bond fluctuation Monte Carlo and Molecular Dynamics methods confirm the original prediction $tausim N^{2 u+1}$, which scales in the same manner as the Rouse relaxation time of the chain except for a larger prefactor, and invalidates other scaling claims.
We investigate the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. An attractive interaction can greatly improve translocation probability. At the same time, it also increases translocation time slowly for weak attraction while exponential dependence is observed for strong attraction. For fixed driving force and chain length the histogram of translocation time has a transition from Gaussian distribution to long-tailed distribution with increasing attraction. Under a weak driving force and a strong attractive force, both the translocation time and the residence time in the pore show a non-monotonic behavior as a function of the chain length. Our simulations results are in good agreement with recent experimental data.
Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the crowding of monomers on the {it trans} - side of the membrane which counterbalance the driving force acting in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent $alpha$ in the translocation time - vs. - chain length scaling law, $tau propto N^{alpha}$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $alpha$ values which were found in experiments and computer simulations.
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