Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an 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) approximately N(1+2nu), 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 defined 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 approximately 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 approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately 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 reveal additional features of dependency on friction.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

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 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 tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Polymer translocation in solid-state nanopores: dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ～ N(2+ν) for the unforced case and as τ ～ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ～ 1/V(α), where α ? 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.     

Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsilonepsilon(c) a finite number N(trans)(t=0) suffices that the translocation probability is close to unity. In the case epsilonepsilon(c), we find that the translocation time scales as tau proportional, variant N(1.65+/-0.08). We suggest a tentative scaling explanation for this result. Also the distribution of translocation times is obtained and discussed.     

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.     

Nondriven Polymer Translocation Through a Nanopore:Scaling for Translocation Time with Chain Length

We investigated the dynamics of the passage for a polymer chain through a nanopore in the absence of any external driving force with Weeks-Chandler-Andersen potential in two-dimensional simulations, in particular, focused our attention on the scaling law of the mean translocation time. We found that the effect of hydrodynamic interactions is the major factor in determining the scaling exponents with increasing pore size. The scaling close to N1+2v was observed when the hydrodynamic interactions were screened in the cases of small pore sizes, while the scaling close to N3v was obtained when the hydrodynamic interactions were present in the cases of large pore sizes.     

Unforced translocation of a polymer chain through a nanopore: the solvent effect

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.     

Heteropolymer translocation through nanopores

The authors investigate the translocation dynamics of heteropolymers driven through a nanopore using a constant temperature Langevin thermostat. Specifically, they 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 AmBn the authors identify both universal as well as specific sequence properties of the translocating chains. They 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. They further discover that for a symmetric heteropolymer AnBn of fixed length, the pattern exhibited by the residence times of the individual monomers has striking similarity with a double slit interference pattern where the total number of repeat units N/2n controls the number of interference fringes. These results are relevant for designing nanopore based sequencing techniques.     

Polymer translocation through a nanopore. II. Excluded volume effect

Following our previous study of a Gaussian chain translocation, we have investigated the transport of a self-avoiding chain from one sphere to another sphere through a narrow pore, using the self-consistent field theory formalism. The free energy landscape for polymer translocation is significantly modified by excluded volume interactions among monomers. The free energy barrier for the placement of one of the chain ends at the pore depends on the chain length N nonmonotonically, in contrast to the N-independence for Gaussian chains. This results in a nonmonotonic dependence of the average arrival time [tau0] on N for self-avoiding chains. When the polymer chain is partitioned between the donor and recipient spheres, a local free energy minimum develops, depending on the strength w of the excluded volume interaction and the relative sizes of the donor and recipient spheres. If the sizes of spheres are comparable, the average translocation time tau (the average time taken by the polymer, after the arrival at the pore, to convert from the donor to the recipient) increases with an increase in w for a fixed N value. On the other hand, for the highly asymmetric sizes of the donor and recipient spheres, tau decreases with an increase in w. As in the case of Gaussian chains, tau depends nonmonotonically on the pore length.     

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, tau, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to tau approximately N(2)D(13). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different tau results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N"D(53)"1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and microchannels.     

Chaperone-assisted translocation of a polymer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy ε between the chaperone and the chain and the chaperone concentration N(c) can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time τ has a transition from a long-tailed distribution to a gaussian distribution with increasing ε. τ rapidly decreases and then almost saturates with increasing binding energy for a short chain; however, it has a minimum for longer chains at a lower chaperone concentration. We also show that τ has a minimum as a function of the chaperone concentration. For different ε, a nonuniversal dependence of τ on the chain length N is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either the crowding effect from a high chaperone concentration or the intersegmental binding for the high binding energy.     

Translocation of α-helix chains through a nanopore

The translocation of α-helix chains through a nanopore is studied through Langevin dynamics simulations. The α-helix chains exhibit several different characteristics about their average translocation times and the α-helix structures when they transport through the nanopores under the driving forces. First, the relationship between average translocation times τ and the chain length N satisfies the scaling law, τ～N(α), and the scaling exponent α depends on the driving force f for the small forces while it is close to the Flory exponent (ν) in the other force regions. For the chains with given chain lengths, it is observed that the dependence of the average translocation times can be expressed as τ～f(-1/2) for the small forces while can be described as τ～f in the large force regions. Second, for the large driving force, the average number of α-helix structures N(h) decreases first and then increases in the translocation process. The average waiting time of each bead, especially of the first bead, is also dependent on the driving forces. Furthermore, an elasticity spring model is presented to reasonably explain the change of the α-helix number during the translocation and its elasticity can be locally damaged by the large driving forces. Our results demonstrate the unique behaviors of α-helix chains transporting through the pores, which can enrich our insights into and knowledge on biopolymers transporting through membranes.     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.     

Sequence effects on the forced translocation of heteropolymers through a small channel

By using a recently developed Monte Carlo algorithm and an exact numerical method, we calculate the translocation probability and the average translocation time for charged heterogeneous polymers driven through a nanopore by an external electric field. The heteropolymer chains are composed of two types of monomers (A and B) which differ only in terms of their electric charge. We present an exhaustive study of chains composed of eight monomers by calculating the average translocation time associated with the 256 possible arrangements for various ratios of the monomer charges (lambda(A)lambda(B)) and electric field intensities E. We find that each sequence leads to a unique value of the translocation probability and time. We also show that the distribution of translocation times is strongly dependent on the two forces felt by the monomers ( approximately lambda(A)E and approximately lambda(B)E). Finally, we present results that highlight the effect of having repetitive patterns by studying the translocation times of various block copolymer structures for a very long chain composed of N=2(18) monomers (all with the same number of A and B monomers).     

Dynamics of polymer translocation into a circular nanocontainer through a nanopore

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 φ, 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 φ. Moreover, we find a nonuniversal scaling exponent of the translocation time as chain length, depending on φ 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.     

The effect of hydrodynamic interactions on the dynamics of DNA translocation through pores

In this work, we investigate the effect of hydrodynamic interactions on the dynamics of DNA translocation through micropores. We simulate DNA as a bead-spring chain and use a lattice Boltzmann method to simulate the flow field that arises from the motion of the molecule. We investigate the free-draining entrance of DNA to the pore by diffusion and find that, consistent with experiments, molecules have a higher probability of entering the pore from one end. We then consider the electric-field driven translocation of 21-210 microm DNA with and without hydrodynamic interactions. Consistent with experiments, we study translocation events that are much shorter than the relaxation time of DNA. We find that the effect of hydrodynamic interactions on this process is to cause different regions of a molecule, other than the ones pulled by voltage or chain connectivity into the pore, to move toward the pore. We quantify this effect and show that it is smaller than the difference in the translocation dynamics of chains that arises from different initial configurations of the molecules. A power-law scaling of translocation time with chain length is observed, with exponents of 1.28+/-0.03 and 1.31+/-0.03 in simulations with and without hydrodynamic interactions, respectively. Our results are in good agreement with recent translocation experiments conducted in small pores and show that, for the regime considered in this work, hydrodynamic interactions play a minor role in the relation of the translocation time to chain length. For fast translocation processes, the effect of hydrodynamic interactions is local and the main factor determining the dynamics of DNA is the initial configuration of the molecules.     

Effect of interaction shape on the condensed toroid of the semiflexible chain

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviors of the mean toroidal and cross sectional radii, rc and rcross, as functions of the contour length L: (rc,rcross) approximately Lnu(Nc), with nu=(1/5,2/5) for the van der Waals-type, nu=(-1/3,2/3) for the Coulomb-type, and nu=(-1,1) for the delta-function-type attractions in the asymptotic limit. For the toroids with finite winding number Nc=100-400, we find nu approximately 0 for the Yukawa interaction with screening parameter kappa=0.5-1.0 and nu=0.1-0.13 for the van der Waals-type interactions. These findings could provide a possible explanation for the experimentally well known observation nu approximately 0 of the condensed DNA toroids. Conformational transitions are also discussed.     

Kinetics of loop formation in polymer chains

We investigate the kinetics of loop formation in ideal flexible polymer chains (the Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is tau(c) approximately tau(0)N(2) (where tau(0) is a microscopic time scale and N is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when a, the capture radius for contact formation, exceeds b, the average distance between two connected beads. Simulations also show that when a < b, tau(c) approximately N(alpha)(tau), where 1.5 < alpha(tau) < or = 2 in the range 7 < N < 200 used in the simulations. By using a diffusion coefficient that is dependent on the length scales a and b (with a < b), which captures the two-stage mechanism by which looping occurs when a < b, we obtain an analytic expression for tauc that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly effected when interactions between monomers are taken into account. Remarkably, for N < 100, the values of tau(c) decrease by more than 2 orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for tau(c) to a power law in N (tau(c) approximately N(alpha)(tau)) show that alpha(tau) varies from about 2.4 in a good solvent to about 1.0 in poor solvents. The effective exponent alpha(tau) decreases as the strength of the attractive monomer-monomer interactions increases. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain. The time for contact formation between beads that are interior to the chain in good solvents changes nonmonotonically as the loop length varies. In contrast, the variation in interior loop closure time is monotonic in poor solvents. The implications of our results for contact formation in polypeptide chains, RNA, and single-stranded DNA are briefly outlined.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献