First passage time distribution of chaperone driven polymer translocation through a nanopore: homopolymer and heteropolymer cases

Combining the advection-diffusion equation approach with Monte Carlo simulations we study chaperone driven polymer translocation of a stiff polymer through a nanopore. We demonstrate that the probability density function of first passage times across the pore depends solely on the Pe?clet number, a dimensionless parameter comparing drift strength and diffusivity. Moreover it is shown that the characteristic exponent in the power-law dependence of the translocation time on the chain length, a function of the chaperone-polymer binding energy, the chaperone concentration, and the chain length, is also effectively determined by the Pe?clet number. We investigate the effect of the chaperone size on the translocation process. In particular, for large chaperone size, the translocation progress and the mean waiting time as function of the reaction coordinate exhibit pronounced sawtooth-shapes. The effects of a heterogeneous polymer sequence on the translocation dynamics is studied in terms of the translocation velocity, the probability distribution for the translocation progress, and the monomer waiting times.     

Factors Affecting Polymer Translocation Through a Nanopore in a Membrane

The variation of the translocation time with respect to the solvent quality was also studied. It showed that there is a transition, as the solvent quality improves from \poor to \good: when ABc, τ increases with increasing AB. When the chain length was changed, it was found that when the absorbed energy u0 was greater than uc, τ was proportional to N1:602; for u0相似文献   

Phase Transition and Oxygen Ion Diffusion in (La1-xLnx)2Mo2O9 (Ln=Nd,Gd, x=0.05-0.25) Using Dielectric Relaxation Method

Monte Carlo simulations were used to study the translocation of a flexible polymer through a pore in a membrane, assuming an attractive interaction between the monomers and the membrane on the trans side of the membrane and no interaction on the cis side. For the case TTc, τ increases with increasing temperature. The translocation time depends on the absorbed energy u0 in a nontrivial way. The value of τ increases initially upon increasing u0 before it begins to decrease.     

The chain sucker: translocation dynamics of a polymer chain into a long narrow channel driven by longitudinal flow

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/microfluidics. During the translocation process if the monomers in the channel can sufficiently quickly assume steady state motion, we observe the scaling τ ～ N∕F of the translocation time τ 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 nonuniversal dependence of τ 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(max), while with increasing the driving force or the channel width the value of s(max) decreases.     

Monte Carlo simulation on polymer translocation in crowded environment

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ~ N(1.25) is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional 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 approximately N2nu for relatively short polymers to tau approximately N1+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 approximately N-nu, which crosses over to v approximately 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 Rg 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 approximately N1+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 approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

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.     

Using an incremental mean first passage approach to explore the viscosity dependent dynamics of the unbiased translocation of a polymer through a nanopore

Noting the limitations of the standard characterization of translocation dynamics, an incremental mean first passage process methodology is used to more completely map the unbiased translocation of a polymer through a nanopore. In this approach, the average time t(0) required to reach successively increasing displacements for the first time is recorded - a measure shown to be more commensurate with the mean first passage nature of translocation. Applying this methodology to the results of Langevin dynamics simulations performed in three dimensions across a range of viscosities, a rich set of dynamics spanning regular diffusion at low viscosities to sub-diffusion at higher viscosities is revealed. Further, while the scaling of the net translocation time τ with polymer length N is shown to be viscosity-dependent, common regimes are found across all viscosities: super-diffusive behaviour at short times, an N-independent backbone consistent with τ ～ N(2.0) at low viscosities and τ ～ N(2.2) at higher viscosities for intermediate times, and N-dependent deviations from the backbone near the completion of translocation.     

Adsorption-driven translocation of polymer chain into nanopores

The polymer translocation into nanopores is generally facilitated by external driving forces, such as electric or hydrodynamic fields, to compensate for entropic restrictions imposed by the confinement. We investigate the dynamics of translocation driven by polymer adsorption to the confining walls that is relevant to chromatographic separation of macromolecules. By using the self-consistent field theory, we study the passage of a chain trough a small opening from cis to trans compartments of spherical shape with adsorption potential applied in the trans compartment. The chain transfer is modeled as the Fokker-Plank diffusion along the free energy landscape of the translocation pass represented as a sum of the free energies of cis and trans parts of the chain tethered to the pore opening. We investigate how the chain length, the size of trans compartment, the magnitude of adsorption potential, and the extent of excluded volume interactions affect the translocation time and its distribution. Interplay of these factors brings about a variety of different translocation regimes. We show that excluded volume interactions within a certain range of adsorption potentials can cause a local minimum on the free energy landscape, which is absent for ideal chains. The adsorption potential always leads to the decrease of the free energy barrier, increasing the probability of successful translocation. However, the translocation time depends non-monotonically of the magnitude of adsorption potential. Our calculations predict the existence of the critical magnitude of adsorption potential, which separates favorable and unfavorable regimes of translocation.     

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.     

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.     

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.     

Theoretical study on the translocation of partially charged polymers through nanopore

The translocation time τ of partially charged polymers through a neutral nanopore is calculated using Fokker–Planck equation with adsorbing–adsorbing boundary conditions. For the polymer with one charged monomer, we find that τ is dependent on the position of the charged monomer and on the magnitude of the driving force f inside the nanopore. When the charge is located at the front half of the polymer chain, τ is larger than that of neutral polymer and increases with f. When the charge is located at the back half, it is smaller than that of the neutral polymer and decreases with increasing f. We have also studied the behavior of a symmetrical polymer with two like charges located symmetrically in the chain and that of an asymmetrical polymer with two unlike charges. Moreover, we have calculated the translocation time for a general condition of polymer with two randomly distributed charges. All results show that τ is dependent on the positions of charges in the polymer chain and on the magnitude of the driving force. The results can be explained qualitatively by the free‐energy landscape of polymer translocation. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1017–1025     

Simulation study on the translocation of a partially charged polymer through a nanopore

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.     

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.     

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.     

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.     

Driven translocation of semiflexible polyelectrolyte through a nanopore

The influence of the chain stiffness on the translocation of semiflexible polyelectrolyte through a nanopore is investigated using Langevin dynamics simulations. Results show that the translocation time τ increases with the bending modulus k_θ because of the increase of viscous drag forces with k_θ. We find that the relation between τ and k_θ, the asymptotic behavior of τ on the polyelectrolyte length N, and the scaling relation between τ and the driving force f are dependent on k_θ and N. Our simulation results show that the semiflexible polyelectrolyte chain can be regarded as either a flexible polyelectrolyte at small k_θ or large N where its radius of gyration R_G is larger than the persistence length L_p or a stiff polyelectrolyte at large k_θ or short N where R_G < L_p. Results also show that the out‐of‐equilibrium effect during the translocation becomes weak with increasing k_θ. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 912–921     

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.     

Cross-streamline migration of a semiflexible polymer in a pressure driven flow

Experiments and simulations on single α-actin filaments in the Poiseuille flow through a microchannel show that the center-of-mass probability density across the channel assumes a bimodal shape as a result of pronounced cross-streamline migration. We reexamine the problem and perform Brownian dynamics simulations for a bead-spring chain with bending elasticity. Hydrodynamic interactions between the pointlike beads are taken into account by the two-wall Green tensor of the Stokes equations. Our simulations reproduce the bimodal distribution only when hydrodynamic interactions are taken into account. Numerical results on the orientational order of the end-to-end vector of the model polymer are also presented together with analytical hard-needle expressions at zero flow velocity. We derive a Smoluchowski equation for the center-of-mass distribution and carefully analyze the different contributions to the probability current that causes the bimodal distribution. As for flexible polymers, hydrodynamic repulsion explains the depletion at the wall. However, in contrast to flexible polymers, the deterministic drift current mainly determines migration away from the centerline and thereby depletion at the center. Diffusional currents due to a position-dependent diffusivity become less important with increasing polymer stiffness.