We consider the dynamics of polymer translocation out of confined environments. Analytic scaling arguments lead to the prediction that the translocation time scales like $τ\sim N^{β+ν_{2D}}R^{1+(1-ν_{2D})/ν}$ for translocation out of a planar confinement between two walls with separation $R$ into a 3D environment, and $τ\sim N^{β+1}R$ for translocation out of two strips with separation $R$ into a 2D environment. Here, $N$ is the chain length, $ν$ and $ν_{2D}$ are the Flory exponents in 3D and 2D, and $β$ is the scaling exponent of translocation velocity with $N$, whose value for the present choice of parameters is $β\approx 0.8$ based on Langevin dynamics simulations. These scaling exponents improve on earlier predictions.
We perform, with the help of cloud computing resources, extensive Langevin simulations which provide compelling evidence in favor of a general markovian framework for unbiased polymer translocation. Our statistical analysis consists of careful evaluations of (i) two-point correlation functions of the translocation coordinate and (ii) the empirical probabilities of complete polymer translocation (taken as a function of the initial number of monomers on a given side of the membrane). We find good agreement with predictions derived from the Markov chain approach recently addressed in the literatu…
We investigate the dynamics of polymer translocation through nanopores under external driving by 3D Langevin Dynamics simulations, focusing on the scaling of the average translocation time $τ$ versus the length of the polymer, $τ\sim N^α$. For slow translocation, i.e., under low driving force and/or high friction, we find $α\approx 1+ν\approx 1.588$ where $ν$ denotes the Flory exponent. In contrast, $α\approx 1.37$ is observed for fast translocation due to the highly deformed chain conformation on the trans side, reflecting a pronounced non-equilibrium situation. The dependence of the transloc…
We perform, with the help of cloud computing resources, extensive Langevin simulations which provide free energy estimates for unbiased three dimensional polymer translocation. We employ the Jarzynski equality in its rigorous setting, to compute the variation of the free energy in single monomer translocation events. In our three-dimensional Langevin simulations, the excluded-volume and van der Waals interactions between beads (monomers and membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic…
Iso-flux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force $f_{\rm c}$. In the high driving force limit, regardless of the channel width, IFTP theory predicts $τ\propto f_{\textrm{c}}^β$ for the translocation time, where $β=-1$ is the force scaling exponent. Moreover, LD data show that for a very narrow channel fitting only a single file of monomers, the entropic force due to the subcha…
We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like particle under the action of an effective potential. Such a model allows us to identify the relevant parameters controlling the polymers dynamics and, in particular, their translocation time. By comparing our analytical results with numerical simulations we show that, under suitable conditions, our model provides reliable predictions of the dynamics of both…
In recent years polymer translocation, i.e., transport of polymeric molecules through nanometer-sized pores and channels embedded in membranes, has witnessed strong advances. It is now possible to observe single-molecule polymer dynamics during the motion through channels with unprecedented spatial and temporal resolution. These striking experimental studies have stimulated many theoretical developments. In this short theory-experiment review, we discuss recent progress in this field with a strong focus on non-equilibrium aspects of polymer dynamics during the translocation process.
The translocation time of a polymer chain through an interaction energy gradient nanopore was studied by Monte Carlo simulations and the Fokker-Planck equation with double-absorbing boundary conditions. Both the simulation and calculation revealed three different behaviors for polymer translocation. These behaviors can be explained qualitatively from free-energy landscapes obtained for polymer translocation at different parameters. Results show that the translocation time of a polymer chain through a nanopore can be tuned by suitably designing the interaction energy gradient.
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…
The theoretical formulation of driven polymer translocation through nanopores is complicated by the combination of the pore electrohydrodynamics and the nonequilibrium polymer dynamics originating from the conformational polymer fluctuations. In this review, we discuss the modeling of polymer translocation in the distinct regimes of short and long polymers where these two effects decouple. For the case of short polymers where polymer fluctuations are negligible, we present a stiff polymer model including the details of the electrohydrodynamic forces on the translocating molecule. We first show…
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 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 …
Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation through a nanochannel embedded in two dimensions under an applied external field. We examine the translocation time for various ratio of the channel length $L$ to the polymer length $N$. For short channels $L\ll N$, the translocation time $τ\sim N^{1+ν}$ under weak driving force $F$, while $τ\sim F^{-1}L$ for long channels $L\gg N$, independent of the chain length $N$. Moreover, we observe a minimum of translocation time as a function of $L/N$ for different driving forces and cha…
DNA translocation through nanopores is one of the most promising strategies for the next-generation sequencing technologies. Most part of experimental and numerical works has focused on polymer translocation biased by electrophoresis, where a pulling force acts on the polymer within the nanopore. An alternative strategy however is emerging, which uses optical or magnetic tweezers. In this case, the pulling force is exerted directly at one end of the polymer, which strongly modifies the translocation process. In this paper, we report numerical simulations of both linear and structured (mimickin…
We perform two-dimensional Langevin dynamics simulations of electric-field driven polymer translocation through an attractive nanopore. We investigate the effect of the location of the attractive region using different pore patterns. This is found to have an impact on both the translocation time as a function of the chain length and on the polymer entry frequency. We qualitatively compare our results to available experimental data.
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 …
Langevin Dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the \textit{trans}-side. Under the influence of pre-stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields …
We study the driven translocation of a flexible polymer through an interacting conical pore using Langevin dynamics simulations. We find that, for a fixed value of externally applied force and pore polymer interaction strength, the mean residence time of monomers inside the pore shows non-monotonic variations with pore apex angle $α$. We explain this behavior using a free energy argument by explicitly accounting for pore-polymer interactions and external drive. Our theoretical observations are corroborated by the simulation results of the mean translocation times as the pore-polymer interactio…
Using Langevin dynamics simulations in three dimensions (3D), we investigate the dynamics of polymer translocation into the regions between two parallel plane walls with separation $R$ under a driving force $F$, respectively. Compared with an unconfined environment, the translocation dynamics is greatly changed due to the crowding effect of the partially translocated monomers. Translocation time $τ$ initially decreases rapidly with increasing $R$ and then saturates for larger $R$, and the confined environment leads to a nonuniversal dependence of $τ$ on $F$.
Single file translocation of a homopolymer through an active channel under the presence of a driving force is studied using Langevin dynamics simulation. It is shown that a channel with sticky walls and oscillating width could lead to significantly more efficient translocation as compared to a static channel that has a width equal to the mean width of the oscillating pore. The gain in translocation exhibits a strong dependence on the stickiness of the pore, which could allow the polymer translocation process to be highly selective.
We study the driven translocation of polymers under time-dependent driving forces using $N$-particle Langevin dynamics simulations. We consider the force to be either sinusoidally oscillating in time or dichotomic noise with exponential correlation time, to mimic both plausible experimental setups and naturally occurring biological conditions. In addition, we consider both the case of purely repulsive polymer-pore interactions and the case with additional attractive polymer-pore interactions, typically occurring inside biological pores. We find that the nature of the interaction fundamentally …
Entropy-driven directed translocation of a flexible polymer through a cone-shaped channel is studied theoretically and using computer simulation. For a given length of the channel, the effective force of entropic origin acting on the polymer is calculated as a function of the apex angle of the channel. It is found that the translocation time is a non-monotonic function of the apex angle. By increasing the apex angle from zero, the translocation time shows a minimum and then a maximum. Also, it is found that regardless of the value of the apex angle, the translocation time is a uniformly decrea…
Polymer translocation experiments typically involve anionic polyelectrolytes such as DNA molecules driven through negatively charged nanopores. Quantitative modelling of polymer capture to the nanopore followed by translocation therefore necessitates the consideration of the electrostatic barrier resulting from like-charge polymer-pore interactions. To this end, in this work we couple mean-field level electrohydrodynamic equations with the Smoluchowski formalism to characterize the interplay between the electrostatic barrier, the electrophoretic drift, and the electro-osmotic liquid flow. In p…
We use a combination of computer simulations and iso-flux tension propagation (IFTP) theory to investigate translocation dynamics of a flexible linear polymer through a nanopore into an environment composed of repulsive active rods in 2D. We demonstrate that the rod activity induces a crowding effect on the polymer, leading to a time-dependent net force that facilitates translocation into the active environment. Incorporating this force into the IFTP theory for pore-driven translocation allows us to characterise translocation dynamics in detail and derive a scaling form for the average translo…
The efficiency of nanopore-based biosequencing techniques requires fast anionic polymer capture by like-charged pores followed by a prolonged translocation process. We show that this condition can be achieved by setting a pressure-solvation trap. Polyvalent cation addition to the KCl solution triggers the like-charge polymer-pore attraction. The attraction speeds-up the pressure-driven polymer capture but also traps the molecule at the pore exit, reducing the polymer capture time and extending the polymer escape time by several orders of magnitude. By direct comparison with translocation exper…
Using Langevin dynamics simulations, we investigate the dynamics of a flexible polymer translocation into a confined area under a driving force through a nanopore. We choose an ellipsoidal shape for the confinement and consider the dependence of the asymmetry of the ellipsoid measured by the aspect ratio on the translocation time. Compared with an isotropic confinement (sphere), an anisotropic confinement (ellipsoid) with the same volume slows down the translocation, and the translocation time increases with increasing the aspect ratio of the ellipsoid. We further find that it takes different …
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 $ε$ 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 $τ$ has a transition from long-tailed distribution to Gaussian distribution with increas…
We study the translocation of a semiflexible polymer through a conical channel with attractive surface interactions and a driving force which varies spatially inside the channel. Using the results of the translocation dynamics of a flexible polymer through an extended channel as control, we first show that the asymmetric shape of the channel gives rise to non-monotonic features in the total translocation time as a function of the apex angle of the channel. The waiting time distributions of individual monomer beads inside the channel show unique features strongly dependent on the driving force …
We review recent progress on the theory of dynamics of polymer translocation through a nanopore based on the iso-flux tension propagation (IFTP) theory. We investigate both pore-driven translocation of flexible and a semi-flexible polymers, and the end-pulled case of flexible chains by means of the IFTP theory and extensive molecular dynamics (MD) simulations. The validity of the IFTP theory can be quantified by the waiting time distributions of the monomers which reveal the details of the dynamics of the translocation process. The IFTP theory allows a parameter-free description of the translo…
We consider the dynamics of a translocation process of a flexible linear polymer through a nanopore into an environment of active rods in the {\it trans} side. Using Langevin dynamics simulations we find that the rods facilitate translocation to the {\it trans} side even when there are initially more monomers on the {\it cis} than on the {\it trans} side. Structural analysis of the translocating polymer reveals that active rods induce a folded structure to the {\it trans}-side subchain in the case of successful translocation events. By keeping the initial number of monomers on the {\it cis}-si…
We investigate the translocation of stiff polymers in the presence of binding particles through a nanopore by two-dimensional Langevin dynamics simulations. We find that the mean translocation time shows a minimum as a function of the binding energy $ε$ and the particle concentration $ϕ$, due to the interplay of the force from binding and the frictional force. Particularly, for the strong binding the translocation proceeds with a decreasing translocation velocity induced by a significant increase of the frictional force. In addition, both $ε$ and $ϕ$ have an notable impact on the distribution …
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…
Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N=21-61. The rate of translocation is controlled by a tunable friction coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length N as <tau_1>~ (N-N_p)^alpha, where N_p is the average number of monomers in the nanopore. The exponent approaches the value alpha=2 when the pore friction is…
We develop a correlation-corrected transport theory in order to predict ionic and polymer transport properties of membrane nanopores in physical conditions where mean-field electrostatics breaks down. The experimentally observed low KCl conductivity of open alpha-Hemolysin pores is quantitatively explained by the presence of surface polarization effects. Upon the penetration of a DNA molecule into the pore, these polarization forces combined with the electroneutrality of DNA sets a lower boundary for the ionic current, explaining the weak salt dependence of blocked pore conductivities at dilut…
Monte Carlo simulations are used to study the translocation of a polymer into and out of a ellipsoidal cavity through a narrow pore. We measure the polymer free energy F as a function of a translocation coordinate, s, defined to be the number of bonds that have entered the cavity. To study polymer insertion, we consider the case of a driving force acting on monomers inside the pore, as well as monomer attraction to the cavity wall. We examine the changes to F(s) upon variation in the shape anisometry and volume of the cavity, the polymer length, and the strength of the interactions driving the…
Here using LAMMPS molecular dynamics (MD) software, we simulate polymer translocation in 2 dimensions. We do the simulations for weak and moderate forces and for different pore diameters. Our results show that in both non-equilibrium and equilibrium initial conditions, translocation time will always increase by increasing binding energy and or increasing pore diameter. Moreover, scaling exponent of time versus force is -0.9531 in accordance to our predecessors. The comparison between equilibrium and non-equilibrium initial condition shows that the translocation time is very sensitive to the in…
We investigate the translocation dynamics of a folded linear polymer which is pulled through a nanopore by an external force. To this end, we generalize the iso-flux tension propagation (IFTP) theory for end-pulled polymer translocation to include the case of two segments of the folded polymer traversing simultaneously trough the pore. Our theory is extensively benchmarked with corresponding Molecular Dynamics (MD) simulations. The translocation process for a folded polymer can be divided into two main stages. In the first stage, both branches are traversing the pore and their dynamics is coup…
