Passage times for polymer translocation pulled through a narrow pore

Crowding induced switching of polymer translocation by the amalgamation of entropy and osmotic pressure

The translocation of polymers is omnipresent in inherently crowded biological systems. We investigate the dynamics of polymer translocation through a pore in free and crowded environments using Langevin dynamics simulation. We observed a location-dependent translocation rate of monomers showcasing counterintuitive behavior in stark contrast to the bead velocity along the polymer backbone. The free energy calculation of asymmetrically placed polymers indicates a critical number of segments to direct receiver-side translocation. For one-sided crowding, we have identified a critical crowding size revealing a nonzero probability of translocation toward the crowded-side. Moreover, we have observed that shifting the polymer toward the crowded-side compensates for one-sided crowding, yielding an equal probability akin to a crowder-free system. In two-sided crowding, a slight variation in crowder size and packing fraction induces a polymer to switch its translocation direction. These conspicuous yet counter-intuitive phenomena are rationalized by minimalistic theoretical arguments based on osmotic pressure and radial entropic forces.

Polymer translocation: effects of periodically driven confinement

We study the influence of confinement on the dynamics of translocation of a linear polymer chain in a good solvent through a cone-shaped pore. Using the Langevin dynamics simulations, we calculate both the first attempt time and translocation time as a function of the position of the back wall and apex angle α. As the in vivo confining environment is inherently dynamic, we extended the present study to explore the consequences of a periodically driven back wall and apex angles on the translocation dynamics. Our findings reveal that the translocation time initially decreases as the driving frequency increases, but increases after a certain frequency. The frequency at which the translocation time is found to be minimum is referred to as the resonance activation. Analyzing the distribution of translocation times around this frequency renders interesting information about the translocation process. We further explore the translocation dynamics by calculating the residence time of individual monomers, shedding light on the microscopic aspects of the process.

Polymer Translocation and Nanopore Sequencing: A Review of Advances and Challenges

Various biological processes involve the translocation of macromolecules across nanopores; these pores are basically protein channels embedded in membranes. Understanding the mechanism of translocation is crucial to a range of technological applications, including DNA sequencing, single molecule detection, and controlled drug delivery. In this spirit, numerous efforts have been made to develop polymer translocation-based sequencing devices, these efforts include findings and insights from theoretical modeling, simulations, and experimental studies. As much as the past and ongoing studies have added to the knowledge, the practical realization of low-cost, high-throughput sequencing devices, however, has still not been realized. There are challenges, the foremost of which is controlling the speed of translocation at the single monomer level, which remain to be addressed in order to use polymer translocation-based methods for sensing applications. In this article, we review the recent studies aimed at developing control over the dynamics of polymer translocation through nanopores.

Polymer Translocation Time

The force- and flow-induced translocation processes of linear and ring polymers are studied using a combination of multiparticle collision dynamics and molecular dynamics, focusing on the behavior of the polymer translocation time. We compare the force- and flow-induced translocations of linear and ring polymers. It is found that when the translocation time (τ*) is characterized by scaling exponents, δ, δ', and α, via the relations τ* ∼ f^δN^α and τ* ∼ J^δ'N^α, the scaling exponents are not constants. For long chains tested, α = 1.0 for both force- and flow-induced translocations. The difference between the force- and flow-induced translocations stems from different monomer crowding effects due to distinct flow patterns outside the channel. Furthermore, general relations for polymer translocation time are derived for these two translocation processes, which are in good agreement with the simulation results. Our results provide clear molecular pictures for the force- and flow-induced translocations, which shed light on the understanding of translocation dynamics and provide guidance for practical applications such as molecular sequencing and ultrafiltration.

Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes and use them to calculate the time evolution of two dynamical quantities for the system, namely, the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times 1≲t≲L^{z_{c}}, where z_{c}=4-η=15/4 is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the generalized Langevin equation with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.

Theory of pore-driven and end-pulled polymer translocation dynamics through a nanopore: an overview

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 translocation process and can be used to derive exact analytic scaling forms in the appropriate limits, including the influence due to the pore friction that appears as a finite-size correction to asymptotic scaling. We show that in the case of pore-driven semi-flexible and end-pulled polymer chains the IFTP theory must be augmented with an explicit trans side friction term for a quantitative description of the translocation process.

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature T_{c}, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼t^{c}, where c is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time-also with exponent c -in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.

Polymer translocation under a pulling force: Scaling arguments and threshold forces

DNA translocation through nanopores is one of the most promising strategies for next-generation sequencing technologies. Most experimental and numerical works have 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 (mimicking DNA) polymer models, simple enough to allow for a statistical treatment of the pore structure effects on the translocation time probability distributions. Based on extremely extended computer simulation data, we (i) propose scaling arguments for an extension of the predicted translocation times τ∼N^{2}F^{-1} over the moderate forces range and (ii) analyze the effect of pore size and polymer structuration on translocation times τ.

Conformation Change, Tension Propagation and Drift-Diffusion Properties of Polyelectrolyte in Nanopore Translocation

Using Langevin dynamics simulations, conformational, mechanical and dynamical properties of charged polymers threading through a nanopore are investigated. The shape descriptors display different variation behaviors for the cis- and trans-side sub-chains, which reflects a strong cis-trans dynamical asymmetry, especially when the driving field is strong. The calculation of bond stretching shows how the bond tension propagates on the chain backbone, and the chain section straightened by the tension force is determined by the ratio of the direct to the contour distances of the monomer to the pore. With the study of the waiting time function, the threading process is divided into the tension-propagation stage and the tail-retraction stage. At the end, the drift velocity, diffusive property and probability density distribution are explored. Owing to the non-equilibrium nature, translocation is not a simple drift-diffusion process, but exhibits several intermediate behaviors, such as ballistic motion, normal diffusion and super diffusion, before ending with the last, negative-diffusion behavior.

Threading DNA through nanopores for biosensing applications

This review outlines the recent achievements in the field of nanopore research. Nanopores are typically used in single-molecule experiments and are believed to have a high potential to realize an ultra-fast and very cheap genome sequencer. Here, the various types of nanopore materials, ranging from biological to 2D nanopores are discussed together with their advantages and disadvantages. These nanopores can utilize different protocols to read out the DNA nucleobases. Although, the first nanopore devices have reached the market, many still have issues which do not allow a full realization of a nanopore sequencer able to sequence the human genome in about a day. Ways to control the DNA, its dynamics and speed as the biomolecule translocates the nanopore in order to increase the signal-to-noise ratio in the reading-out process are examined in this review. Finally, the advantages, as well as the drawbacks in distinguishing the DNA nucleotides, i.e., the genetic information, are presented in view of their importance in the field of nanopore sequencing.

Polymer translocation: the first two decades and the recent diversification

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.

Transient behaviour of a polymer dragged through a viscoelastic medium

We study the dynamics of a polymer that is pulled by a constant force through a viscoelastic medium. This is a model for a polymer being pulled through a cell by an external force, or for an active biopolymer moving due to a self-generated force. Using the Rouse model with a memory dependent drag force, we find that the center of mass of the polymer follows a subballistic motion. We determine the time evolution of the length and the shape of the polymer. Through an analysis of the velocity of the monomers, we investigate how the tension propagates through the polymer. We discuss how polymers can be used to probe the properties of a viscoelastic medium.

Through the eye of the needle: recent advances in understanding biopolymer translocation

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.

Translocation dynamics of a short polymer driven by an oscillating force

We study the translocation dynamics of a short polymer moving in a noisy environment and driven by an oscillating force. The dynamics is numerically investigated by solving a Langevin equation in a two-dimensional domain. We consider a phenomenological cubic potential with a metastable state to model the polymer-pore interaction and the entropic free energy barrier characterizing the translocation process. The mean first translocation time of the center of inertia of polymers shows a nonmonotonic behavior, with a minimum, as a function of the number of the monomers. The dependence of the mean translocation time on the polymer chain length shows a monotonically increasing behavior for high values of the number of monomers. Moreover, the translocation time shows a minimum as a function of the frequency of the oscillating forcing field for all the polymer lengths investigated. This finding represents the evidence of the resonant activation phenomenon in the dynamics of polymer translocation, whose occurrence is maintained for different values of the noise intensity.

Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions

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 affects the translocation dynamics. For the non-attractive pore, the translocation time crosses over to a fast translocation regime as the frequency of the driving force decreases. In the attractive pore case, because of a free energy well induced inside the pore, the translocation time can be a minimum at the optimal frequency of the force, the so-called resonant activation. In the latter case, we examine the effect of various physical parameters on the resonant activation, and explain our observations using simple theoretical arguments.

Propagation of tension along a polymer chain

We study the propagation of tension caused by an external force along a long polymeric molecule in two different settings, namely along a free polymer in three-dimensional (3D) space being pulled from one end, and along a prestretched circular polymer, confined in a narrow circular tube. We show that in both cases, the tension propagation is governed by a diffusion equation, and in particular, the tension front propagates as t(1/2) along the contour of the chain. The results are confirmed numerically, and by molecular dynamics simulations in the case of the 3D polymer. We also compare our results with the previously suggested ones for the translocation setting, and discuss why tension propagation is slower in that case.

Flow-induced translocation of polymers through a fluidic channel: a dissipative particle dynamics simulation study

The dynamics of flow-induced translocation of polymers through a fluidic channel has been studied by dissipative particle dynamics (DPD) approach. Unlike implicit solvent models, the many-body energetic and hydrodynamic interactions are preserved naturally by incorporating explicit solvent particles in this approach. The no-slip wall boundary and the adaptive boundary conditions have been implemented in the modified DPD approach to model the hydrodynamic flow within a specific wall structure of fluidic channel and control the particles' density fluctuations. The results show that the average translocation time versus polymer chain length satisfies a power-law scaling of τ ∼N(1.152). The conformational changes and translocation dynamics of polymers through the fluidic channel have also been investigated in our simulations, and two different translocation processes, i.e., the single-file and double-folded translocation events, have been observed in detail. These findings may be helpful in understanding the conformational and dynamic behaviors of such polymer and/or DNA molecules during the translocation processes.

Force-driven polymer translocation through a nanopore: an old problem revisited

We consider DNA translocation through a pore in a planar membrane. The pore is so narrow that only one DNA segment can fit in. Assuming that the biasing force f acts inside the pore only, and that the DNA monomer number N is asymptotically large, we modify the previously developed treatment of the stretched part of the pre-translocated polymer by introducing the concept of "iso-flux trumpet". We show that friction of a moving chain in the trumpet, although it determines the speed of the process, provides only a marginal fraction of overall dissipation in the process. The dominant dissipation turns out to be due to irreversible entropic squeezing of the chain into the small pore. We also discover that because of the role of the membrane a much larger amount of heat of order k(B)T per monomer gets transferred from the heat bath on the post-translocation side to that on the pre-translocation side.

Single-polymer dynamics under constraints: scaling theory and computer experiment

The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces--a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.

Probabilistic phase space trajectory description for anomalous polymer dynamics

It has been recently shown that the phase space trajectories for the anomalous dynamics of a tagged monomer of a polymer--for single polymeric systems and phenomena such as phantom Rouse, self-avoiding Rouse, and Zimm ones, reptation, and translocation through a narrow pore in a membrane, as well as for many polymeric systems such as polymer melts in the entangled regime--are robustly described by the generalized Langevin equation. Here I show that the probability distribution of phase space trajectories for all of these classical anomalous dynamics for single polymers is that of a fractional Brownian motion (fBm), while the dynamics for polymer melts between the entangled regime and the eventual diffusive regime exhibits small but systematic deviations from that of a fBm.

Fractional Brownian motion approach to polymer translocation: the governing equation of motion

We suggest a governing equation that 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 subdiffusive increase of the distribution variance Δ(t) with elapsed time Δ(t)∝t(α). The latter quantity measures the mean-squared number s of polymer segments that have passed through the pore Δ(t)=([s(t)-s(t=0)](2)), and is known to grow with an anomalous diffusion exponent α<1. Our main assumption [i.e., a Gaussian distribution of the translocation velocity v(t)] and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation, which we performed in 3D. We also numerically confirm the predictions made recently that the exponent α changes from 0.91 to 0.55 to 0.91 for short-, intermediate-, and long-time regimes, respectively.

Resonant activation in polymer translocation: new insights into the escape dynamics of molecules driven by an oscillating field

The translocation of molecules across cellular membranes or through synthetic nanopores is strongly affected by thermal fluctuations. In this work we study how the dynamics of a polymer in a noisy environment changes when the translocation process is driven by an oscillating electric field. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics, by taking into account the harmonic interactions between adjacent monomers and the excluded-volume effect by introducing a Lennard-Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion. Thermal fluctuations are taken into account by introducing a Gaussian uncorrelated noise. The mean first translocation time of the polymer centre of inertia shows a minimum as a function of the frequency of the oscillating forcing field. This finding represents the first evidence of the resonant activation behaviour in the dynamics of polymer translocation.

Amplitude and frequency spectra of thermal fluctuations of a translocating RNA molecule

Using a combination of theory and computer simulations, we study the translocation of an RNA molecule, pulled through a solid-state nanopore by an optical tweezer, as a method for determining its secondary structure. The resolution with which the elements of the secondary structure can be determined is limited by thermal fluctuations. We present a detailed study of these thermal fluctuations, including the frequency spectrum, and show that these rule out single-nucleotide resolution under the experimental conditions which we simulated. Two possible ways to improve this resolution are strongly stretching the RNA with a back-pulling voltage across the membrane, and stiffening the translocated part of the RNA by biochemical means.

Non-equilibrium dynamics of single polymer adsorption to solid surfaces

The adsorption of polymers to surfaces is crucial for understanding many fundamental processes in nature. Recent experimental studies indicate that the adsorption dynamics is dominated by non-equilibrium effects. We investigate the adsorption of a single polymer of length N to a planar solid surface in the absence of hydrodynamic interactions. We find that for weak adsorption energies the adsorption timescales ∼N((1+2ν)/(1+ν)), where ν is the Flory exponent for the polymer. We argue that in this regime the single chain adsorption is closely related to a field-driven polymer translocation through narrow pores. Surprisingly, for high adsorption energies the adsorption time becomes longer, as it scales as ∼N(1+ν), which is explained by strong stretching of the unadsorbed part of the polymer close to the adsorbing surface. These two dynamic regimes are separated by an energy scale that is characterized by non-equilibrium contributions during the adsorption process.

Comment on 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and other recent papers by D Panja, G Barkema and R Ball

In a recent publication of Panja et al (2007 J. Phys.: Condens. Matter 19 432202) they suggested a new interpretation of the translocation problem of polymer chain threading through a narrow pore. Here we point out some contradictions and inconsistencies in this treatment which question the plausibility of the obtained results.

Reply to the comment on 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and other recent papers by D Panja, G Barkema and R Ball

We reply to the comment made by Dubbeldam et al (2009 J. Phys.: Condens. Matter 21 098001) on our paper 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and our other recent papers.

Response of single polymers to localized step strains

In this paper, the response of single three-dimensional phantom and self-avoiding polymers to localized step strains are studied for two cases in the absence of hydrodynamic interactions: (i) Polymers tethered at one end with the strain created at the point of tether, and (ii) free polymers with the strain created in the middle of the polymer. The polymers are assumed to be in their equilibrium state before the step strain is created. It is shown that the strain relaxes as a power law in time t as t(-eta). While the strain relaxes as 1/t for the phantom polymer in both cases; the self-avoiding polymer relaxes its strain differently in case (i) than in case (ii): As t(-(1+nu)/(1+2nu)) and as t(-2/(1+2nu)), respectively. Here nu is the Flory exponent for the polymer, with value approximately 0.588 in three dimensions. Using the mode expansion method, exact derivations are provided for the 1/t strain relaxation behavior for the phantom polymer. However, since the mode expansion method for self-avoiding polymers is nonlinear, similar theoretical derivations for the self-avoiding polymer proves difficult to provide. Only simulation data are therefore presented in support of the t(-(1+nu)/(1+2nu)) and the t(-2/(1+2nu)) behavior. The relevance of these exponents for the anomalous dynamics of polymers is also discussed.

Translocation dynamics with attractive nanopore-polymer interactions

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 tau approximately tau1+tau2+tau3 corresponding to the initial filling of the pore, transfer of polymer from the cis side to the trans side, and emptying of the pore, respectively. We find that the dynamics for the last process of emptying of the pore changes from nonactivated to activated in nature as the strength of the attractive interaction increases, and tau3 becomes the dominant contribution to the total translocation time for strong attraction. This leads to nonuniversal dependence of tau as a function of driving force and chain length. Our results are in good agreement with recent experimental findings, and provide a plausible explanation for the different scaling behavior observed in solid state nanopores vs that for the natural alpha-hemolysin channel.

Dynamics of DNA translocation through an attractive nanopore

We investigate the dynamics of single-stranded DNA translocation through a nanopore driven by an external force using Langevin dynamics simulations in two dimensions 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, 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 AmCn, we find that the translocation time decreases exponentially as a function of the volume fraction fC of the base C. For longer A sequences with fC<or=0.5, the translocation time strongly depends on the orientation of DNA, namely which base enters the pore first. Our studies clearly demonstrate that for a DNA of certain length N with repeat units AmCn, the pattern exhibited by the waiting times of the individual bases and their periodicity can unambiguously determine the values of m, n, and N, respectively. Therefore, a prospective experimental realization of this phenomenon may lead to fast and efficient sequence detection.

Effect of charge distribution on the translocation of an inhomogeneously charged polymer through a nanopore

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 being at the midpoint of the chain for a rodlike polymer and close to the leading chain end for an ideal chain. The presence of attractive and repulsive pore-charge interactions yields a shift in the optimum charge position toward the trailing end and the leading end of the chain, respectively. Moreover, our results show that strong attractive or repulsive interactions between the charge and the pore lengthen the translocation time relative to translocation through an inert pore. We generalize our results to accommodate the presence of multiple charged sites on the polymer. Our results provide insight into the effect of charge inhomogeneity on protein translocation through biological membranes.