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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 time for polymer translocation into the same ellipsoid through major-axis and minor-axis directions, depending on the average density of the whole chain in the ellipsoid, $\phi$. For $\phi$ lower than a critical value $\phi_c$, the translocation through minor axis is faster, and vice versa. These complicated behaviors are interpreted by the degree of the confinement and anisotropic confinement induced folding of the translocated chain., Comment: 8 pages, 7 figures, accepted to Soft Matter

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 $\epsilon$ and the particle concentration $\phi$, 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 $\epsilon$ and $\phi$ have an notable impact on the distribution of the translocation time. With increasing $\epsilon$ and $\phi$, it undergoes a transition from an asymmetric and broad distribution under the weak binding to a nearly Gaussian one under the strong binding, and its width becomes gradually narrower., Comment: 7 pages, 6 figures, accepted to J. Chem. Phys

We investigate the chain conformation of ring polymers confined to a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. We predict that the longitudinal size of a ring polymer scales with the chain length and the diameter of the channel in the same manner as that for linear chains based on scaling analysis and Flory-type theory. Moreover, Flory-type theory also gives the ratio of the longitudinal sizes for a ring polymer and a linear chain with identical chain length. These theoretical predictions are confirmed by numerical simulations. Finally, our simulation results show that this ratio first decreases and then saturates with increasing the chain stiffness, which has interpreted the discrepancy in experiments. Our results have biological significance., Comment: 5 pages, 3 figures

Using Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a circular nanocontainer through a nanopore under a driving force $F$. We observe that the translocation probability initially increases and then saturates with increasing $F$, independent of $\phi$, which is the average density of the whole chain in the nanocontainer. The translocation time distribution undergoes a transition from a Gaussian distribution to an asymmetric distribution with increasing $\phi$. Moreover, we find a nonuniversal scaling exponent of the translocation time as chain length, depending on $\phi$ and $F$. These results are interpreted by the conformation of the translocated chain in the nanocontainer and the time of an individual segment passing through the pore during translocation., Comment: 9 pages, 12 figures

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 $\tau \sim N^{1+\nu}$ under weak driving force $F$, while $\tau\sim F^{-1}L$ 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 channel widths. These results are interpreted by the waiting time of a single segment., Comment: 7 pages, 10 figures

We investigate the ejection dynamics of a ring polymer out of a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. The ejection dynamics for ring polymers shows two regimes like for linear polymers, depending on the relative length of the chain compared with the channel. For long chains with length $N$ larger than the critical chain length $N_{c}$, at which the chain just fully occupies the nanochannel, the ejection for ring polymers is faster compared with linear chains of identical length due to a larger entropic pulling force; while for short chains ($N

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy $\epsilon$ between the chaperone and the chain and the chaperone concentration $N_c$ can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time $\tau$ has a transition from long-tailed distribution to Gaussian distribution with increasing $\epsilon$. $\tau$ rapidly decreases and then almost saturates with increasing binding energy for short chain, however, it has a minimum for longer chains at lower chaperone concentration. We also show that $\tau$ has a minimum as a function of the chaperone concentration. For different $\epsilon$, a nonuniversal dependence of $\tau$ on the chain length $N$ is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either crowding effect from high chaperone concentration or the intersegmental binding for the high binding energy., Comment: 10 pages, to appear in J. Am. Chem. Soc

Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a narrow channel of width $R$ embedded in two dimensions, driven by a force proportional to the number of monomers in the channel. Such a setup mimics typical experimental situations in nano/micro-fluidics. During the the translocation process if the monomers in the channel can sufficiently quickly assume steady state motion, we observe the scaling $\tau\sim N/F$ of the translocation time $\tau$ with the driving force $F$ per bead and the number $N$ of monomers per chain. With smaller channel width $R$, steady state motion cannot be achieved, effecting a non-universal dependence of $\tau$ on $N$ and $F$. From the simulations we also deduce the waiting time distributions under various conditions for the single segment passage through the channel entrance. For different chain lengths but the same driving force, the curves of the waiting time as a function of the translocation coordinate $s$ feature a maximum located at identical $s_{\mathrm{max}}$, while with increasing the driving force or the channel width the value of $s_{\mathrm{max}}$ decreases., Comment: 9 pages, 14 figures. To appear in J. Chem. Phys

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 $\tau$ on the chain length $N$. $\tau$ initially decreases rapidly and then saturates with increasing $R$, and a dependence of the scaling exponent $\alpha$ of $\tau$ with $N$ on the channel width $R$ is observed. The otherwise inverse linear scaling of $\tau$ with $F$ breaks down and we observe a minimum of $\alpha$ 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., Comment: 8 pages, 12 figures. To appear in Phys. Rev. E

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 $\tau$ initially decreases rapidly with increasing $R$ and then saturates for larger $R$, and the confined environment leads to a nonuniversal dependence of $\tau$ on $F$., Comment: 7pages, 11 figures

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 $\tau$ versus the length of the polymer, $\tau\sim N^{\alpha}$. For slow translocation, i.e., under low driving force and/or high friction, we find $\alpha \approx 1+\nu \approx 1.588$ where $\nu$ denotes the Flory exponent. In contrast, $\alpha\approx 1.37$ 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 translocation time on the driving force is given by $\tau \sim F^{-1}$ and $\tau \sim F^{-0.80}$ for slow and fast translocation, respectively. These results clarify the controversy on the magnitude of the scaling exponent $\alpha$ for driven translocation., Comment: 6 pages, 7 figures, to appear in EPL (Europhysics Letters)

We consider the dynamics of polymer translocation out of confined environments. Analytic scaling arguments lead to the prediction that the translocation time scales like $\tau\sim N^{\beta+\nu_{2D}}R^{1+(1-\nu_{2D})/\nu}$ for translocation out of a planar confinement between two walls with separation $R$ into a 3D environment, and $\tau \sim N^{\beta+1}R$ for translocation out of two strips with separation $R$ into a 2D environment. Here, $N$ is the chain length, $\nu$ and $\nu_{2D}$ are the Flory exponents in 3D and 2D, and $\beta$ is the scaling exponent of translocation velocity with $N$, whose value for the present choice of parameters is $\beta \approx 0.8$ based on Langevin dynamics simulations. These scaling exponents improve on earlier predictions., Comment: 5 pages, 5 figures. To appear in Phys. Rev. E

We investigate the dynamics of DNA translocation through a nanopore driven by an external force using Langevin dynamics simulations in two dimensions (2D) to study how the translocation dynamics depend on the details of the DNA sequences. We consider a coarse-grained model of DNA built from two bases $A$ and $C$, having different base-pore interactions, {\textit e.g.}, a strong (weak) attractive force between the pore and the base $A$ ($C$) inside the pore. From a series of studies on hetero-DNAs with repeat units $A_mC_n$, we find that the translocation time decreases exponentially as a function of the volume fraction $f_C$ of the base $C$. %($\epsilon_{pC} < \epsilon_{pA}$). For longer $A$ sequences with $f_C \le 0.5$, 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 $A_mC_n$, 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 technic., Comment: 7 pages, 7 figures

We investigate several scaling properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulation in three dimension (3D). Specifically motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we determine the chain length dependence of the scaling exponents of the average translocation time, the average velocity of the center of mass, $$, the effective radius of gyration during the translocation process, and the scaling exponent of the translocation coordinate ($s$-coordinate) as a function of the translocation time. We further discuss the possibility that in the case of driven translocation the finite pore size and its geometry could be responsible that the veclocity scaling exponent is less than unity and discuss the dependence of the scaling exponents on the pore geometry for the range of $N$ studied here., Comment: 6 pages, 4 figures. Submitted to J. Chem. Phys

We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time $\tau \sim N^{\alpha}$ and the mean-square change of the PT coordinate $ \sim t^\beta$. We find $\alpha=1+2\nu$ and $\beta=2/\alpha$ for unbiased PT in 2D and 3D. The relation $\alpha \beta=2$ holds for driven PT in 2D, with crossover from $\alpha \approx 2\nu$ for short chains to $\alpha \approx 1+\nu$ for long chains. This crossover is, however, absent in 3D where $\alpha = 1.42 \pm 0.01$ and $\alpha \beta \approx 2.2$ for $N \approx 40-800$., Comment: 4 pages, 4 figures, minor changes in the text, To be published in: Phys. Rev. E 78, xxxxxx(R) (2008)

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 $\tau \approx \tau_1+\tau_2+\tau_3$ corresponding to the initial filling of the pore, transfer of polymer from the \textit{cis} side to the \textit{trans} side, and emptying of the pore, respectively. We find that the dynamics for the last process of emptying of the pore changes from non-activated to activated in nature as the strength of the attractive interaction increases, and $\tau_3$ becomes the dominant contribution to the total translocation time for strong attraction. This leads to a new 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 possible explanation for the different scaling behavior observed in solid state nanopores {\it vs.} that for the natural $\alpha$-hemolysin channel., Comment: 8 pages, 11 figures

We investigate the dynamics of DNA translocation through a nanopore using 2D Langevin dynamics simulations, focusing on the dependence of the translocation dynamics on the details of DNA sequences. The DNA molecules studied in this work are built from two types of bases $A$ and $C$, which has been shown previously to have different interactions with the pore. We study DNA with repeating blocks $A_nC_n$ for various values of $n$, and find that the translocation time depends strongly on the {\em block length} $2n$ as well as on the {\em orientation} of which base entering the pore first. Thus, we demonstrate that the measurement of translocation dynamics of DNA through nanopore can yield detailed information about its structure. We have also found that the periodicity of the block sequences are contained in the periodicity of the residence time of the individual nucleotides inside the pore., Comment: 4 pages, 4 figures, minor changes

One of the most fundamental quantities associated with polymer translocation through a nanopore is the translocation time $\tau$ and its dependence on the chain length $N$. Our simulation results based on both the bond fluctuation Monte Carlo and Molecular Dynamics methods confirm the original prediction $\tau\sim N^{2\nu+1}$, which scales in the same manner as the Rouse relaxation time of the chain except for a larger prefactor, and invalidates other scaling claims., Comment: 1+pages, 1 Figure, Minor changes

We investigate the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. An attractive interaction can greatly improve translocation probability. At the same time, it also increases translocation time slowly for weak attraction while exponential dependence is observed for strong attraction. For fixed driving force and chain length the histogram of translocation time has a transition from Gaussian distribution to long-tailed distribution with increasing attraction. Under a weak driving force and a strong attractive force, both the translocation time and the residence time in the pore show a non-monotonic behavior as a function of the chain length. Our simulations results are in good agreement with recent experimental data., Comment: 4 pages, 5 figures, Submitted to Phys. Rev. Lett

We investigate the translocation dynamics of heteropolymers driven through a nanopore using a constant temperature Langevin thermostat. Specifically, we consider heteropolymers consisting of two types of monomers labeled A and B, which are distinguished by the magnitude of the driving force that they experience inside the pore. From a series of studies on polymers with sequences AnBn+m we identify both universal as well as sequence specific properties of the translocating chains. We find that the scaling of the average translocation time as a function of the chain length N remains unaffected by the heterogeneity, while the residence time of each bead is a strong function of the sequence for short repeat units. We further discover that for a symmetric heteropolymer AnBn of fixed length, the pattern exhibited by the residence time of the individual monomer has striking similarity with an interference pattern for an optical grating with N/(2n) slits. These results are relevant for designing nanopore based sequencing techniques., Comment: 13 Pages, 6 Figures

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time $\tau_e$ required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that $\tau_e$ scales with the chain length $N$ as $\tau_e \sim N^{1+2\nu}$, where $\nu $ is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient $\xi$, the driving force $E$ and the length of the chain $N$ on the translocation time $\tau$, which is defind as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and $\tau \sim E^{-1}$. The influence of $\xi$ depends on the ratio between the driving and frictional forces. For intermediate $\xi$, we find a crossover scaling for $\tau$ with $N$ from $\tau \sim N^{2\nu}$ for relatively short chains to $\tau \sim N^{1 + \nu}$ for longer chains. However, for higher $\xi$, only $\tau \sim N^{1 + \nu}$ is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing $\xi$ increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveals additional features of dependency on friction., Comment: submitted to J. Chem. Phys., 8 pages with 10 figures

We investigate polymer translocation through a nanopore under a pulling force using Langevin dynamics simulations. We concentrate on the influence of the chain length $N$ and the pulling force $F$ on the translocation time $\tau$. The distribution of $\tau$ is symmetric and narrow for strong $F$. We find that $\tau\sim N^{2}$ and translocation velocity $v\sim N^{-1}$ for both moderate and strong $F$. For infinitely wide pores, three regimes are observed for $\tau$ as a function of $F$. With increasing $F$, $\tau$ is independent of $F$ for weak $F$, and then $\tau\sim F^{-2+\nu^{-1}}$ for moderate $F$, where $\nu$ is the Flory exponent, which finally crosses over to $\tau\sim F^{-1}$ for strong force. For narrow pores, even for moderate force $\tau\sim F^{-1}$. Finally, the waiting time, for monomer $s$ and monomer $s+1$ to exit the pore, has a maximum for $s$ close to the end of the chain, in contrast to the case where polymer is driven by an external force within the pore., Comment: submitted, 7 pages with 5 figures. To appear in PRE

The morphology and dynamics of polymerization-induced phase separation in the initially homogeneous solution of a non-reactive component in reactive monomers are investigated by incorporating the reaction kinetics into the time-dependent Ginzburg Landau equation. Analytical results show that there is a reduction of the initial length scale in the early stage of phase separation. The reason is the increase of the molecule weight of emerging polymer, independent of the fact whether the system goes through the metastable region or not. The numerical results are in good agreement with theoretical prediction quite well., Comment: 20 pages, 6 figures. European Polymer Journal, 2006 (in press)

We study the dynamics and equilibrium profile shapes of contact lines for wetting in the case of a spatially inhomogeneous solid wall with stripe defects. Using a phase-field model with conserved dynamics, we first numerically determine the contact line behavior in the case of a stripe defect of varying width. For narrow defects, we find that the maximum distortion of the contact line and the healing length are related to the defect width, while for wide defects, they saturate to constant values. This behavior is in quantitative agreement with experimental data. In addition, we examine the shape of the contact line between two stripe defects as a function of their separation. Using the phase-field model, we also analytically estimate the contact line configuration, and find good qualitative agreement with the numerical results., Comment: 25 pages, 8 figures

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the 2D fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength $E$, length of the chain $N$, and length of the pore $L$ on forced translocation. As our main result, we find a crossover scaling for the translocation time $\tau $ with the chain length from $\tau \sim N^{2\nu}$ for relatively short polymers to $\tau \sim N^{1 + \nu}$ for longer chains, where $\nu $ is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains $v \sim N^{- \nu}$, which crosses over to $v \sim N^{- 1}$ for long polymers. The reason for this is that with increasing $N$ there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which $R_\parallel $, the radius of gyration $R_{g}$ along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large $N$, however, the asymptotic scaling $\tau \sim N^{1 + \nu}$ is recovered. In this regime, $\tau $ is almost independent of $L$. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for $R_\parallel \approx L$. We show here that this minimum persists for a weak fields $E$ such that $EL$ is less than some critical value, but vanishes for large values of $EL$., Comment: 25 Pages, 10 figures. Submitted to J. Chem. Phys. J. Chem. Phys. 124, in press (2006)

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional (2D) fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore, and study the escape time required for the polymer to completely exit the pore on either end. In particular, we examined the effect of the pore length on the escape time., Comment: 16Pages, 6 figures