A Monte Carlo algorithm to study polymer translocation through nanopores. I. Theory and numerical approach

Homopolymer and heteropolymer translocation through patterned pores under fluctuating forces

We investigate the translocation of a semiflexible polymer through extended patterned pores using Langevin dynamics simulations, specifically focusing on the influence of a time-dependent driving force. Our findings reveal that, akin to its flexible counterpart, a rigid chain-like molecule translocates faster when subjected to an oscillating force than a constant force of equivalent average magnitude. The enhanced translocation is strongly correlated with the stiffness of the polymer and the stickiness of the pores. The arrangement of the pores plays a pivotal role in translocation dynamics, deeply influenced by the interplay between polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness, the oscillating force introduces significant variations in the translocation time distributions based on segment sizes and orientations. On the basis of these insights, we propose a sequencing approach that harnesses distinct pore surface properties that are capable of accurately predicting sequences in heteropolymers with diverse bending rigidities.

Gain reversal in the translocation dynamics of a semiflexible polymer through a flickering pore

We study the driven translocation of a semiflexible polymer through an attractive extended pore with a periodically oscillating width. Similar to its flexible counterpart, a stiff polymer translocates through an oscillating pore more quickly than a static pore whose width is equal to the oscillating pore's mean width. This efficiency quantified as a gain in the translocation time, highlights a considerable dependence of the translocation dynamics on the stiffness of the polymer and the attractive nature of the pore. The gain characteristics for various polymer stiffness exhibit a trend reversal when the stickiness of the pore is changed. The gain reduces with increasing stiffness for a lower attractive strength of the pore, whereas it increases with increasing stiffness for higher attractive strengths. Such a dependence leads to the possibility of a high degree of robust selectivity in the translocation process.

Molecular Dynamics Simulation of a Single Carbon Chain through an Asymmetric Double-Layer Graphene Nanopore for Prolonging the Translocation Time

In recent years, sensing technology based on nanopores has become one of the trustworthy options for characterization and even identification of a single biomolecule. In nanopore based DNA sequencing technology, the DNA strand in the electrolyte solution passes through the nanopore under an applied bias electric field. Commonly, the ionic current signals carrying the sequence information are difficult to detect effectively due to the fast translocation speed of the DNA strand, so that slowing down the translocation speed is expected to make the signals easier to distinguish and improve the sequencing accuracy. Modifying the nanopore structure is one of the effective methods. Through all-atom molecular dynamics simulations, we designed an asymmetric double-layer graphene nanopore structure to regulate the translocation speed of a single carbon chain. The structure consists of two nanopores with different sizes located on two layers. The simulation results indicate that the asymmetric nanopore structure will affect the chain's translocation speed and the ionic current value. When the single carbon chain passes from the smaller pore to the larger pore, the translocation time is significantly prolonged, which is about three times as long as the chain passing from the larger pore to the smaller pore. These results provide a new idea for designing more accurate and effective single-molecule solid-state nanopore sensors.

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.

Driven translocation of a semi-flexible polymer through a nanopore

We study the driven translocation of a semi-flexible polymer through a nanopore by means of a modified version of the iso-flux tension propagation theory, and extensive molecular dynamics (MD) simulations. We show that in contrast to fully flexible chains, for semi-flexible polymers with a finite persistence length [Formula: see text] the trans side friction must be explicitly taken into account to properly describe the translocation process. In addition, the scaling of the end-to-end distance R N as a function of the chain length N must be known. To this end, we first derive a semi-analytic scaling form for R N, which reproduces the limits of a rod, an ideal chain, and an excluded volume chain in the appropriate limits. We then quantitatively characterize the nature of the trans side friction based on MD simulations. Augmented with these two factors, the theory shows that there are three main regimes for the scaling of the average translocation time τ ∝ N α . In the rod [Formula: see text], Gaussian [Formula: see text] and excluded volume chain [Formula: see text] ≫ 10 6 limits, α = 2, 3/2 and 1 + ν, respectively, where ν is the Flory exponent. Our results are in good agreement with available simulations and experimental data.

Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts

The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.

Analysis of the lattice kinetic Monte Carlo method in systems with external fields

The lattice kinetic Monte Carlo (LKMC) method is studied in the context of Brownian particles subjected to drift forces, here principally represented by external fluid flow. LKMC rate expressions for particle hopping are derived that satisfy detailed balance at equilibrium while also providing correct dynamical trajectories in advective-diffusive situations. Error analyses are performed for systems in which collections of particles undergo Brownian motion while also being advected by plug and parabolic flows. We demonstrate how the flow intensity, and its associated drift force, as well as its gradient, each impact the accuracy of the method in relation to reference analytical solutions and Brownian dynamics simulations. Finally, we show how a non-uniform grid that everywhere retains full microscopic detail may be employed to increase the computational efficiency of lattice kinetic Monte Carlo simulations of particles subjected to drift forces arising from the presence of external fields.

Evaluating the applicability of the Fokker-Planck equation in polymer translocation: a Brownian dynamics study

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, γ0p, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length as <τ1> ∼ (N - Np)(α), where Np is the average number of monomers in the nanopore. The exponent approaches the value α = 2 when the pore friction is sufficiently high, in accord with the prediction for the case of the quasi-static regime where pore friction dominates. In the case of forced translocation, the polymer chain is stretched and compressed on the cis and trans sides, respectively, for low γ0p. However, the chain approaches conformational quasi-equilibrium for sufficiently large γ0p. In this limit the observed scaling of <τ1> with driving force and chain length supports the Fokker-Planck (FP) prediction that <τ> ∝ N/fd for sufficiently strong driving force. Monte Carlo simulations are used to calculate translocation free energy functions for the system. The free energies are used with the FP equation to calculate translocation time distributions. At sufficiently high γ0p, the predicted distributions are in excellent agreement with those calculated from the BD simulations. Thus, the FP equation provides a valid description of translocation dynamics for sufficiently high pore friction for the range of polymer lengths considered here. Increasing N will require a corresponding increase in pore friction to maintain the validity of the FP approach. Outside the regime of low N and high pore friction, the polymer is out of equilibrium, and the FP approach is not valid.

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.

Driven translocation of a semi-flexible chain through a nanopore: a Brownian dynamics simulation study in two dimensions

We study translocation dynamics of a semi-flexible polymer chain through a nanoscopic pore in two dimensions using Langevin dynamics simulation in presence of an external bias F inside the pore. For chain length N and stiffness parameter κb considered in this paper, we observe that the mean first passage time <τ> increases as <τ(κb)>~<τ(κb=0)>lp(aN) , where κb and lp are the stiffness parameter and persistence length, respectively, and aN is a constant that has a weak N dependence. We monitor the time dependence of the last monomer xN(t) at the cis compartment and calculate the tension propagation time (TP) ttp directly from simulation data for <xN(t)> ~ t as alluded in recent nonequlibrium TP theory [T. Sakaue, Phys. Rev. E 76, 021803 (2007)] and its modifications to Brownian dynamics tension propagation theory [T. Ikonen, A. Bhattacharya, T. Ala-Nissila, and W. Sung, Phys. Rev. E 85, 051803 (2012); and J. Chem. Phys. 137, 085101 (2012)] originally developed to study translocation of a fully flexible chain. We also measure ttp from peak position of the waiting time distribution W(s) of the translocation coordinate s (i.e., the monomer inside the pore), and explicitly demonstrate the underlying TP picture along the chain backbone of a translocating chain to be valid for semi-flexible chains as well. From the simulation data, we determine the dependence of ttp on chain persistence length lp and show that the ratio ttp∕<τ> is independent of the bias F.

Polymer translocation dynamics in the quasi-static limit

Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to <τ> ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.

Translocation of a polymer through a nanopore across a viscosity gradient

The translocation of a polymer through a pore in a membrane separating fluids of different viscosities is studied via several computational approaches. Starting with the polymer halfway, we find that as a viscosity difference across the pore is introduced, translocation will predominately occur towards one side of the membrane. These results suggest an intrinsic pumping mechanism for translocation across cell walls which could arise whenever the fluid across the membrane is inhomogeneous. Somewhat surprisingly, the sign of the preferred direction of translocation is found to be strongly dependent on the simulation algorithm: for Langevin dynamics (LD) simulations, a bias towards the low viscosity side is found while for Brownian dynamics (BD), a bias towards the high viscosity is found. Examining the translocation dynamics in detail across a wide range of viscosity gradients and developing a simple force model to estimate the magnitude of the bias, the LD results are demonstrated to be more physically realistic. The LD results are also compared to those generated from a simple, one-dimensional random walk model of translocation to investigate the role of the internal degrees of freedom of the polymer and the entropic barrier. To conclude, the scaling of the results across different polymer lengths demonstrates the saturation of the directional preference with polymer length and the nontrivial location of the maximum in the exponent corresponding to the scaling of the translocation time with polymer length.

Separating different polymers using an interacting nanopore: a Monte Carlo study

Translocation of a multi-polymer system containing two kinds of polymers, polymer A and polymer B, through an interacting nanopore is studied using dynamic Monte Carlo method. Polymer A and polymer B have different polymer-pore interactions. The probability of one kind of polymer first translocating through a nanopore is dependent on the polymer-pore interactions and the magnitude of driving force for monomers inside the nanopore. At weak driving, there are separation regions where one kind of polymer translocates through the pore always before another kind of polymer. A phase diagram containing separation regions and mixed region is presented. At last, the first-in first-out rule for the polymer translocation is investigated.

Translocation of a polymer through a nanopore modulated by a sticky site

Using a one-dimensional model for the translocation of a polymer through a nanopore, the effect of a "sticky site" at which the polymer binds to the pore is explored via exact numerical techniques. Results for the mean translocation time and the probability of translocation on the insertion of the first monomer in the pore are generated across a wide range of driving forces and binding potential strengths (well depths). The balance between the driving force, diffusion, and well depth yields a rich set of dynamics that depend strongly on where the sticky site is located along the polymer. For example, when the sticky site is located near the head of the polymer, the translocation time is found to be a maximum at an intermediate driving force with events at lower driving forces taking less time. Additionally, the critical well depth at which the sticky site dominates the dynamics, is found to be a non-monotonic function of the driving force when the sticky site is located at the head or tail of the polymer, but not in the middle. Modeling of the process yields good agreement with simulation results.

Influence of non-universal effects on dynamical scaling in driven polymer translocation

We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the cis side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.

Translocation of a heterogeneous polymer

We present results on the sequence dependence of translocation kinetics for a partially charged heteropolymer moving through a very thin pore using theoretical tools and Langevin dynamics simulational techniques. The chain is composed of two types of monomers of differing frictional interaction with the pore and charge. We present exact analytical expressions for passage probability, mean first passage time, and mean successful passage times for both reflecting/absorbing and absorbing/absorbing boundary conditions, showing rich and unexpected dependence of translocation behavior on charge fraction, distribution along the chain, and electric field configuration. We find excellent qualitative and good quantitative agreement between theoretical and simulation results. Surprisingly, there emerges a threshold charge fraction of a diblock copolymer beyond which the success rate of translocation is independent of charge fraction. Also, the mean successful translocation time of a diblock copolymer displays non-monotonic behavior with increasing length of the charged block; there is an optimum length of the charged block where the mean translocation rate is the slowest; and there can be a substantial range of higher charge fractions which make the translocation slower than even a minimally charged chain. Additionally, we find for a fixed total charge on the chain, finer distribution along the backbone significantly decreases mean translocation time.

Unifying model of driven polymer translocation

We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by solving the model for chain lengths up to 10^{10} monomers, we show that the chain lengths probed by experiments and simulations are typically orders of magnitude below the asymptotic limit. This explains both the considerable scatter in the observed scaling of translocation time with respect to chain length, and some of the shortcomings of present theories. Our study shows that for a quantitative theory of polymer translocation, explicit consideration of finite chain length effects is required.

Optimizing the accuracy of lattice Monte Carlo algorithms for simulating diffusion

The behavior of a lattice Monte Carlo (LMC) algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for unbiased particle diffusion that if one of these two parameters remains fixed, the accuracy of the algorithm is optimal for a certain finite value of the other parameter. In one dimension, the optimal algorithm with moves to the two nearest neighbor sites reproduces the correct second and fourth moments (and minimizes the error for the higher moments at large times) of the particle distribution and preserves the first two moments of the first-passage time distributions. In two and three dimensions, the same level of accuracy requires simultaneous moves along two axes ("diagonal" moves). Such moves attempting to cross an impenetrable boundary should be projected along the boundary, rather than simply rejected. We also treat the case of absorbing boundaries. We discuss the relation between optimally accurate LMC algorithms and a particular case of lattice Boltzmann (LB) algorithms for simulating diffusion and compare the computational efficiency of optimal LMC and optimal LB algorithms.

A kinetic analysis of protein transport through the anthrax toxin channel

Anthrax toxin is composed of three proteins: a translocase heptameric channel, (PA₆₃)₇, formed from protective antigen (PA), which allows the other two proteins, lethal factor (LF) and edema factor (EF), to translocate across a host cell’s endosomal membrane, disrupting cellular homeostasis. (PA₆₃)₇ incorporated into planar phospholipid bilayer membranes forms a channel capable of transporting LF and EF. Protein translocation through the channel can be driven by voltage on a timescale of seconds. A characteristic of the translocation of LF_N, the N-terminal 263 residues of LF, is its S-shaped kinetics. Because all of the translocation experiments reported in the literature have been performed with more than one LF_N molecule bound to most of the channels, it is not clear whether the S-shaped kinetics are an intrinsic characteristic of translocation kinetics or are merely a consequence of the translocation in tandem of two or three LF_Ns. In this paper, we show both in macroscopic and single-channel experiments that even with only one LF_N bound to the channel, the translocation kinetics are S shaped. As expected, the translocation rate is slower with more than one LF_N bound. We also present a simple electrodiffusion model of translocation in which LF_N is represented as a charged rod that moves subject to both Brownian motion and an applied electric field. The cumulative distribution of first-passage times of the rod past the end of the channel displays S-shaped kinetics with a voltage dependence in agreement with experimental data.

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.

Escape of polymer chains from an attractive channel under electrical force

The escape of polymer chains from an attractive channel under external electrical field is studied using dynamical Monte Carlo method. Though the escaping process is nonequilibrium in nature, results show that the one-dimensional diffusion theoretical model based on the equilibrium assumption can describe the dependence of the average escaping time (τ(0)) on the polymer-channel interaction (ɛ), the electrical field (E), the chain length (n), and the channel length (L), qualitatively. Results indicate that both ɛ and E play very important roles in the escaping dynamics. For small ɛ, the polymer chain moves out of the channel continuously and quickly. While for large ɛ, the polymer chain is difficult to move out of long channels as it is trapped for a long time (τ(trap)) when the end segment is near the critical point x(C). These results are consistent with the theoretical results for the free energy profiles at small ɛ and large ɛ, respectively. The dependence of x(C) and τ(trap) on ɛ and E are discussed, and specific relations are obtained. The configurational properties of polymer chain are also investigated during the escaping process.

Polymer translocation induced by a bad solvent

We study polymer translocation through a nanopore subject to conformational differences created by putting two different solvents at the cis and trans compartments using Langevin dynamics in three dimensions (3D). Initially a fraction of the chain is placed in a good solvent at the cis side and the rest of the chain at the trans side is immersed in a bad solvent where it forms a globule. We study several aspects of the translocating chain as a function of the strength of the interaction ɛ/k(B)T for the bad solvent, where the temperature T is kept below the Θ temperature for the specific bead-spring model that we have used to describe the chain. For ɛ/k(B)T≥1 we find the mean first passage time (τ)~(ɛ/k(B)T)(-1) and (τ)~N(1.1±0.05). In that regard, translocation under solvent asymmetry is similar to the case of driven translocation under a bias inside the pore. However, the globule formed at the trans in the immediate vicinity of the pore readily absorbs the incoming particles making the translocation process faster than the driven translocation. Our simulation results for long chains and ɛ/k(B)T≥1 agree well with a theoretical prediction by Muthukumar [M. Muthukumar, J. Chem. Phys. 111, 10371 (1999).].

The distribution of DNA translocation times in solid-state nanopores

This paper systematically investigates the effects of solution viscosity, applied voltage and DNA chain length on the distribution of DNA translocation times through 8 ± 2 nm diameter silicon nitride nanopores. Linear dsDNA translocation events were selected based on the magnitude of current blockage and accumulated into scatter plots of current blockage and event duration (translocation time). The translocation time distribution was fitted to the solution of a Smoluchowski-type equation for 1D biased diffusion to a sink. The DNA drifting speed under bias and diffusion constant were extracted from the fits as functions of solution viscosity, applied voltage and DNA chain length. Combined with the Einstein-Smoluchowski relation, this model allowed evaluation of the viscous drag force on DNA molecules. This model also allowed estimation of the uncertainty in determining the DNA chain length due to the influence of friction on the spread of translocation times in a nanopore measurement. The data analysis suggests that the simple 1D biased diffusion model fits the experimental data well for a wide range of conditions. Some deviations from predicted behavior were observed and show where additional phenomena are likely to contribute to the distribution of DNA translocation times.

Cooperative translocation dynamics of biopolymer chains through nanopores in a membrane: Slow dynamics limit

The cooperative translocation dynamics of two complementary single-stranded DNA chains through two nanopores located in a membrane is investigated theoretically. The translocation process is considered to be quasi-equilibrium, and then under the limit of slow dynamics the average translocation times are numerically presented under different conditions. It is shown that the effects of the chemical potential gradient, the recombination energy and the distance between the two nanopores on the cooperative translocation are significant. The present model predicts that the cooperative translocation of such two chains can shorten the translocation time, reduce the backward motion and thus improve the translocation efficiency.

Polymer translocation into a fluidic channel through a nanopore

Using two-dimensional Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a fluidic channel with diameter R through a nanopore under a driving force F . Due to the crowding effect induced by the partially translocated monomers, the translocation dynamics is significantly altered in comparison to an unconfined environment, namely, we observe a nonuniversal dependence of the translocation time τ on the chain length N . τ initially decreases rapidly and then saturates with increasing R , and a dependence of the scaling exponent α of τ with N on the channel width R is observed. The otherwise inverse linear scaling of τ with F breaks down and we observe a minimum of α as a function of F . These behaviors are interpreted in terms of the waiting time of an individual segment passing through the pore during translocation.

Out-of-equilibrium characteristics of a forced translocating chain through a nanopore

Polymer translocation through a nanopore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the cis and the trans side separately either as a function of the time during the translocation process or as as function of the monomer index m inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the cis side are distinctly different from those at the trans side. During the translocation and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier and the chain immediately after translocation is described by an effective Flory exponent 0.45+/-0.01. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the cis to the trans side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (N) of the average translocation time <tau>, the average velocity of the center of mass <vCM>, and the effective radius of gyration <Rg> during the translocation process defined as <tau> approximately Nalpha, <vCM> approximately N(-delta), and Rg approximately Nnu respectively, and the exponent of the translocation coordinate (s-coordinate) as a function of the translocation time <s2(t)> approximately tbeta. We find alpha = 1.36 +/- 0.01, beta = 1.60+/- 0.01 for <s2(t)> approximately taubeta and beta = 1.44 +/- 0.02 for <Deltas2(t)> approximately taubeta, delta = 0.81 +/- 0.04, and nu congruent with nu = 0.59 +/- 0.01, where nu is the equilibrium Flory exponent in 3D. Therefore, we find that <tau> approximately N1.36 is consistent with the estimate of <tau> approximately <Rg>/<vCM>. However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent alpha = 1.36 +/- 0.01 < 1 + nu. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the "cis" and "trans" parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.

On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part I: Analytical model and characteristic analysis

We develop two models to describe ion transport in variable-height micro- and nanochannels. For the first model, we obtain a one-dimensional (unsteady) partial differential equation governing flow and charge transport through a shallow and wide electrokinetic channel. In this model, the effects of electric double layer (EDL) on axial transport are taken into account using exact solutions of the Poisson-Boltzmann equation. The second simpler model, which is approachable analytically, assumes that the EDLs are confined to near-wall regions. Using a characteristics analysis, we show that the latter model captures concentration polarization (CP) effects and provides useful insight into its dynamics. Two distinct CP regimes are identified: CP with propagation in which enrichment and depletion shocks propagate outward, and CP without propagation where polarization effects stay local to micro- nanochannel interfaces. The existence of each regime is found to depend on a nanochannel Dukhin number and mobility of the co-ion nondimensionalized by electroosmotic mobility. Interestingly, microchannel dimensions and axial diffusion are found to play an insignificant role in determining whether CP propagates. The steady state condition of propagating CP is shown to be controlled by channel heights, surface chemistry, and co-ion mobility instead of the reservoir condition. Both models are validated against experimental results in Part II of this two-paper series.

DNA unhooking from a single post as a deterministic process: insights from translocation modeling

Using stochastic methods developed for DNA translocation through nanopores, we study the unhooking of a long DNA chain from an isolated stationary micropost. Such methods quickly and efficiently furnish both the full probability distribution of the unhooking time and the ensuing moments for a wide range of chain and field parameters. The results compare favorably to more realistic but computationally intense Brownian dynamics simulations. For typical chain lengths and applied electric fields used in experiments, the unhooking process is effectively deterministic; diffusive fluctuations make a negligible contribution to the first and second moments of the unhooking time. This result lends credence to continuous-time random-walk models of the overall transport process that treat the unhooking as a convective process.