We have used Langevin dynamics to simulate the forced translocation of linked polymer rings through a narrow pore. For fixed size (i.e. fixed number of monomers) the translocation time depends on the link type and on whether the rings are knotted or unknotted. For links with two unknotted rings, the crossings between the rings can slow down the translocation and are responsible for a delay as the crossings pass through the pore. The results fall on a set of relatively smooth curves for different link families with the translocation time not always increasing with crossings number within the same family. When one ring is knotted the results depend on whether the link is prime or composite and, for the composite case, they depend on whether the knotted or unknotted ring enters the pore first. We find a similar situation for 3-component links where the results depend on whether the link is prime or composite. These results contribute to our understanding of how the entanglement complexity between filaments impacts their translocation dynamics and should be useful for extending nanopore-sensing techniques to probe the topological properties of these systems.
We study the translocation process of a polymer in the absence of external fields for various pore diameters $b$ and membrane thickness $L$. The polymer performs Rouse and reptation dynamics. The mean translocation time $<τ_t>$ that the polymer needs to escape from a cell, and the mean dwell time $<τ_d>$ that the polymer spends in the pore during the translocation process, obey scaling relations in terms of the polymer length $N$, $L$ and $b/R_g$, where $R_g$ is the radius of gyration for the polymer. We explain these relations using simple arguments based on polymer dynamics and the equilibri…
We study pore blockade times for a translocating polymer of length $N$, driven by a field $E$ across the pore in three dimensions. The polymer performs Rouse dynamics, i.e., we consider polymer dynamics in the absence of hydrodynamical interactions. We find that the typical time the pore remains blocked during a translocation event scales as $\sim N^{(1+2ν)/(1+ν)}/E$, where $ν\simeq0.588$ is the Flory exponent for the polymer. In line with our previous work, we show that this scaling behaviour stems from the polymer dynamics at the immediate vicinity of the pore -- in particular, the memory ef…
We consider a polymer of length $N$ translocating through a narrow pore in the absence of external fields. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $τ_{R}\sim N^{1+2ν}$, with a mean square displacement through the pore consistent with $t^{(1+ν)/(1+2ν)}$, with $ν\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{-(1+ν)/(1+2ν)}\exp(-t/τ_{R})$. Beyond the Rouse time translocation becomes diffusiv…
We propose a method for the theoretical investigation of polymer translocation through composite pore structures possessing arbitrarily specified geometries. Translocation through each constituent part of the composite is treated as being analogous to the diffusion of the translocation coordinate over the free energy landscape derived from the chain configurations within the pore. The proposed method accounts for possible reverse motions of the leading chain end at the interface between constituent parts of a composite pore, a possibility that has been neglected in prior studies. As an illustr…
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 translocatio…
Theoretical derivation and numerical confirmation are provided for the scaling of pore-blockade times as $N^{2+ν}$ for unbiased translocation in two and three dimensions, with $N$ as the polymer length and $ν$ as the Flory exponent of the polymer. The polymer performs Rouse dynamics.
We study the passage times of a translocating polymer of length $N$ in three dimensions, while it is pulled through a narrow pore with a constant force $F$ applied to one end of the polymer. At small to moderate forces, satisfying the condition $FN^ν/k_BT\lesssim1$, where $ν\approx0.588$ is the Flory exponent for the polymer, we find that $τ_N$, the mean time the polymer takes to leave the pore, scales as $N^{2+ν}$ independent of $F$, in agreement with our earlier result for F=0. At strong forces, i.e., for $FN^ν/k_BT\gg1$, the behaviour of the passage time crosses over to $τ_N\sim N^2/F$. We …
In this paper, we investigate the microscopic dynamics of a polymer of length $N$ translocating through a narrow pore. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $τ_{R}\sim N^{1+2ν}$, with a mean square displacement through the pore consistent with $t^{(1+ν)/(1+2ν)}$, with $ν\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{-(1+ν)/(1+2ν)}\exp(-t/τ_{R})$. Beyond the Rouse time translocation beco…
We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional (2D) fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore, and study the escape time required for the polymer to completely exit the pore on either end. In particular, we examined the effect of the pore length on the escape time.
One of the most fundamental quantities associated with polymer translocation through a nanopore is the translocation time $τ$ 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 $τ\sim N^{2ν+1}$, which scales in the same manner as the Rouse relaxation time of the chain except for a larger prefactor, and invalidates other scaling claims.
Polymer translocation through a nanopore in a membrane investigated theoretically. Recent experiments on voltage-driven DNA and RNA translocations through a nanopore indicate that the size and geometry of the pore are important factors in polymer dynamics. A theoretical approach is presented which explicitly takes into account the effect of the nanopore length and diameter for polymer motion across the membrane. It is shown that the length of the pore is crucial for polymer translocation dynamics. The present model predicts that for realistic conditions (long nanopores and large external field…
We investigate the voltage-driven translocation of an inhomogeneously charged polymer through a nanopore by utilizing discrete and continuous stochastic models. As a simplified illustration of the effect of charge distribution on translocation, we consider the translocation of a polymer with a single charged site in the presence and absence of interactions between the charge and the pore. We find that the position of the charge that minimizes the translocation time in the absence of pore--polymer interactions is determined by the entropic cost of translocation, with the optimum charge position…
I did off-lattice 3D Monte Carlo simulations for polymer translocation through a narrow pore at low external field, trying to be as close to a direct approach as possible. The process was found non equilibrium globally, but dynamics of the monomers close to the pore (the fold) was found close to quasi equilibrium. I observed a tension (or pressure) buildup near the pore, and subdiffusion for the displacement of the middle monomer in the pore, as reported in the literature. I did not find the distribution of the reaction coordinate after some time of free diffusion predicted by the fractional d…
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…
We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the 2D fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength $E$, length of the chain $N$, and length of the pore $L$ on forced translocation. As our main result, we find a crossover scaling for the translocation time $τ$ with the chain length from $τ\sim N^{2ν}$ for relatively short polymers to $τ\sim N^{1 + ν}$ for longer chains, where $ν$ is the Flory exponent. We demonstrate that this crossover is due to the change in …
Using Langevin dynamics simulations, we investigate the influence of polymer-pore interactions on the dynamics of biopolymer translocation through nanopores. We find that an attractive interaction can significantly change the translocation dynamics. This can be understood by examining the three components of the total translocation time $τ\approx τ_1+τ_2+τ_3$ corresponding to the initial filling of the pore, transfer of polymer from the \textit{cis} side to the \textit{trans} side, and emptying of the pore, respectively. We find that the dynamics for the last process of emptying of the pore ch…
Using continuous time Monte-Carlo method we simulated the translocation of a polynucleotide chain driven through a nanopore by an electric field. We have used two models of driven diffusion due to the electric field. The chain may have strong interaction with the pore, and depends on which end of the chain first enters the pore. Depending on this interaction, in both cases, the distribution of times for the chain to pass through the pore in our model is found to have three peaks, as observed in the experiment of Kasianowicz, Brandin, Branton and Deamer (KBBD).
We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition probabilities which satisfy a specific balance constraint provide a refinement of the Chuang-Kantor-Kardar relaxation picture of translocation, allowing us to investigate finite size effects in the evaluation of dynamical scaling exponents. We find that (i) previous Langevin simulation results can be recovered only if corrections to the polymer mobility exponent are…
We investigate the dynamics of DNA translocation through a nanopore using 2D Langevin dynamics simulations, focusing on the dependence of the translocation dynamics on the details of DNA sequences. The DNA molecules studied in this work are built from two types of bases $A$ and $C$, which has been shown previously to have different interactions with the pore. We study DNA with repeating blocks $A_nC_n$ for various values of $n$, and find that the translocation time depends strongly on the {\em block length} $2n$ as well as on the {\em orientation} of which base entering the pore first. Thus, w…
We investigate polymer translocation through a nanopore under a pulling force using Langevin dynamics simulations. We concentrate on the influence of the chain length $N$ and the pulling force $F$ on the translocation time $τ$. The distribution of $τ$ is symmetric and narrow for strong $F$. We find that $τ\sim N^{2}$ and translocation velocity $v\sim N^{-1}$ for both moderate and strong $F$. For infinitely wide pores, three regimes are observed for $τ$ as a function of $F$. With increasing $F$, $τ$ is independent of $F$ for weak $F$, and then $τ\sim F^{-2+ν^{-1}}$ for moderate $F$, where $ν$ i…
We investigate the dynamics of DNA translocation through a nanopore driven by an external force using Langevin dynamics simulations in two dimensions (2D) to study how the translocation dynamics depend on the details of the DNA sequences. We consider a coarse-grained model of DNA built from two bases $A$ and $C$, having different base-pore interactions, {\textit e.g.}, a strong (weak) attractive force between the pore and the base $A$ ($C$) inside the pore. From a series of studies on hetero-DNAs with repeat units $A_mC_n$, we find that the translocation time decreases exponentially as a funct…
The transport of polymers with folded configurations across membrane pores is investigated theoretically by analyzing simple discrete stochastic models. The translocation dynamics is viewed as a sequence of two events: motion of the folded segment through the channel followed by the linear part of the polymer. The transition rates vary for the folded and linear segments because of different interactions between the polymer molecule and the pore. It is shown that the translocation time depends non-monotonously on the length of the folded segment for short polymers and weak external fields, whil…
Motivated by identifying the origin of the bias dependence of tension propagation we investigate methods for measuring tension propagation quantitatively in computer simulations of driven polymer translocation. Here the motion of flexible polymer chains through a narrow pore is simulated using Langevin dynamics. We measure tension forces, bead velocities, bead distances, and bond angles along the polymer at all stages of translocation with unprecedented precision. Measurements are done at a standard temperature used in simulations and at zero temperature to pin down the effect of fluctuations.…
The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence…
The translocation of a macromolecule through a nanometer-sized pore is an interesting process with important applications in the development of biosensors for single--molecule analysis and in drug delivery and gene therapy. We have carried out a molecular dynamics simulation study of electrophoretic translocation of a charged polymer through an artificial nanopore to explore the feasibility of semiconductor--based nanopore devices for ultra--fast DNA sequencing. The polymer is represented by a simple bead--spring model designed to yield an appropriate coarse-grained description of the phosphat…
We study the effect of the crowded nature of the cellular cytoplasm on the translocation of a polymer through a pore in a membrane. By systematically treating the entropic penalty due to crowding, we show that the translocation dynamics are significantly altered, leading to novel scaling behaviors of the translocation time in terms of chain length. We also observe new and qualitatively different translocation regimes depending upon the extent of crowding, transmembrane chemical potential asymmetry, and polymer length.
We study voltage driven translocation of a single stranded (ss) DNA through a membrane channel. Our model, based on a master equation (ME) approach, investigates the probability density function (pdf) of the translocation times, and shows that it can be either double or mono-peaked, depending on the system parameters. We show that the most probable translocation time is proportional to the polymer length, and inversely proportional to the first or second power of the voltage, depending on the initial conditions. The model recovers experimental observations on hetro-polymers when using their pr…
We use the Bond Fluctuation Model (BFM) to study the pore-blockade times of a translocating polymer of length $N$ in two dimensions, in the absence of external forces on the polymer (i.e., unbiased translocation) and hydrodynamic interactions (i.e., the polymer is a Rouse polymer), through a narrow pore. Earlier studies using the BFM concluded that the pore-blockade time scales with polymer length as $τ_d \sim N^β$, with $β=1+2ν$, whereas some recent studies with different polymer models produce results consistent with $β=2+ν$, originally predicted by us. Here $ν$ is the Flory exponent of the …
This paper reports the force spectroscopy analysis of a polymer that translocates from one side of a membrane to the other side through an extended pore, pulled by a cantilever that moves with constant velocity against the damping and the potential barrier generated by the reaction of the membrane walls. The polymer is modeled as a beads-springs chain with both excluded volume and bending contributions, and moves in a stochastic three dimensional environment described by a Langevin dynamics at fixed temperature. The force trajectories recorded at different velocities reveal two unexplored expo…
For single-file translocations of a charged macromolecule through a narrow pore, the crucial step of arrival of an end at the pore suffers from free energy barriers, arising from changes in intrachain electrostatic interaction, distribution of ionic clouds and solvent molecules, and conformational entropy of the chain. All contributing factors to the barrier in the initial stage of translocation are evaluated by using the self-consistent field theory for the polyelectrolyte and the coupled Poisson-Boltzmann description for ions, without radial symmetry. The barrier is found to be essentially e…
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 $τ\propto N_0^{1+ν}$, where $N_0$ 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 $N_0^{2ν}$ exactly cancel o…
We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This result enables us to construct the mean translocation velocity demonstrating that translocation is faster when the adsorbing particles are smaller. Monte-Carlo simulations also show that smaller particles gives less dispersion in the ratchete…
We suggest a governing equation which describes the process of polymer chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time $t$ after the process has begun, and (ii) a sub-diffusive increase of the distribution variance $Δ(t)$ with elapsed time, $Δ(t) \propto t^α$. The latter quantity measures the mean-squared number $s$ of polymer segments which have passed through the pore, $Δ(t) = <[s(t)-s(t=0)]^2>$, and is known to grow with an anomalous …
Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for the probability density function of the chemical coordinate matches the initial-stage subdiffusive regime and takes into account the equilibrium entropic drive. Precise scaling relations connect the subdiffusion exponent to the divergence with the polymer length of the translocation time, and also to the singularity of the probability density function at the…
We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P , its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. …
We propose to model the stochastic dynamics of a polymer passing through a pore (translocation) by means of a fractional Brownian motion, and study its behavior in presence of an absorbing boundary. Based on scaling arguments and numerical simulations, we present a conjecture that provides a link between the persistence exponent $θ$ and the Hurst exponent $H$ of the process, thus sheding light on the spatial and temporal features of translocation. Furthermore, we show that this conjecture applies more generally to a broad class of self affine processes undergoing anomalous diffusion in bounded…
