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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.
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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.
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 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.
Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy $epsilon$ between the chaperone and the chain and the chaperone concentration $N_c$ can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time $tau$ has a transition from long-tailed distribution to Gaussian distribution with increasing $epsilon$. $tau$ rapidly decreases and then almost saturates with increasing binding energy for short chain, however, it has a minimum for longer chains at lower chaperone concentration. We also show that $tau$ has a minimum as a function of the chaperone concentration. For different $epsilon$, a nonuniversal dependence of $tau$ on the chain length $N$ is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either crowding effect from high chaperone concentration or the intersegmental binding for the high binding energy.
The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $alpha = 2/(2 u+2-gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $<s(t)>$, and $<s^2(t)> - < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.
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