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Register a new userTheory of polymer translocation through a flickering nanopore under an alternating driving force
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We develop a theory for polymer translocation driven by a time-dependent force through an oscillating nanopore. To this end, we extend the iso-flux tension propagation theory (IFTP) [Sarabadani textit{et al., J. Chem. Phys.}, 2014, textbf{141}, 214907] for such a setup. We assume that the external driving force in the pore has a component oscillating in time, and the flickering pore is similarly described by an oscillating term in the pore friction. In addition to numerically solving the model, we derive analytical approximations that are in good agreement with the numerical simulations. Our results show that by controlling either the force or pore oscillations, the translocation process can be either sped up or slowed down depending on the frequency of the oscillations and the characteristic time scale of the process. We also show that while in the low and high frequency limits the translocation time $tau$ follows the established scaling relation with respect to chain length $N_0$, in the intermediate frequency regime small periodic fluctuations can have drastic effects on the dynamical scaling. The results can be easily generalized for non-periodic oscillations and elucidate the role of time dependent forces and pore oscillations in driven polymer translocation.
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We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {em anomalous} diffusive behavior even in the {em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $alpha = 2/(2 u +2 - gamma_1)$, where $ u$ is the Flory exponent and $gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $tau propto f^{-1}N^{frac{2}{alpha} -1}$. Also the corresponding time dependent statistical moments, $< s(t) > propto t^{alpha}$ and $< s(t)^2 > propto t^{2alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.
We investigate the translocation of a single stranded DNA through a pore which fluctuates between two conformations, using coupled master equations. The probability density function of the first passage times (FPT) of the translocation process is calculated, displaying a triple, double or mono peaked behavior, depending on the interconversion rates between the conformations, the applied electric field, and the initial conditions. The cumulative probability function of the FPT, in a field-free environment, is shown to have two regimes, characterized by fast and slow timescales. An analytical expression for the mean first passage time of the translocation process is derived, and provides, in addition to the interconversion rates, an extensive characterization of the translocation process. Relationships to experimental observations are discussed.
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.
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 $N approx 40-800$.
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