Translocation of polymer chains through interacting nanopores

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

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

Translocation of a looped polymer threading through a nanopore

Recent experiments reported that the complicated translocation dynamics of a looped DNA chain through a nanopore can be detected by ionic current blockade profiles. Inspired by the experimental results, we systematically study the translocation dynamics of a looped polymer, formed by three building blocks of a loop in the middle and two tails of the same length connected with the loop, by using Langevin dynamics simulations. Based on two entering modes (tail-leading and loop-leading) and three translocation orders (loop-tail-tail, tail-loop-tail, and tail-tail-loop), the translocation of the looped polymer is classified into six translocation pathways, corresponding to different current blockade profiles. The probabilities of the six translocation pathways are dependent on the loop length, polymer length, and pore radius. Moreover, the translocation times of the entire polymer and the loop are investigated. We find that the two translocation times show different dependencies on the translocation pathways and on the lengths of the loop and the entire polymer.

Simulation study on the migration of diblock copolymers in periodically patterned slits

The forced migration of diblock copolymers (A_NAB_NB) in periodically patterned slits was investigated by using Langevin dynamics simulation. The lower surface of the slit consists of stripe α and stripe β distributed in alternating sequence, while the upper one is formed only by stripe β. The interaction between block A and stripe α is strongly attractive, while all other interactions are purely repulsive. Simulation results show that the migration of the diblock copolymer is remarkably dependent on the driving force and there is a transition region at moderate driving force. The transition driving force f_t, where the transition region occurs, decreases monotonously with increasing length of block B (N_B) but is independent of the polymer length and the periodic length of the slit, which is interpreted from the free energy landscape of diblock copolymer migration. The results also show that periodic slits could be used to separate diblock polymers with different N_B by tuning the external driving force.

Trapped and non-trapped polymer translocations through a spherical pore

The polymer translocation through a spherical pore is studied using the Langevin dynamics simulation. The translocation events are classified into two types: one is the trapped translocation in which the entire polymer is trapped in the pore and the other is the non-trapped translocation where the pore cannot hold the whole polymer. We find that the trapped translocation is favored at large spheres and small external voltages. However, the monomer-pore attraction would lead to the non-monotonic behavior of the trapped translocation possibility out of all translocation events. Moreover, both the trapped and non-trapped translocation times are dependent on the polymer length, pore size, external voltage, and the monomer-pore attraction. There exist two pathways for the polymer in the trapped translocation: an actively trapped pathway for the polymer trapped in the pore before the head monomer arrives at the pore exit, and a passively trapped pathway for the polymer trapped in the pore while the head monomer is struggling to move out of the pore. The studies of trapped pathways can provide a deep understanding of the polymer translocation behavior.

Effects of solvent quality and non-equilibrium conformations on polymer translocation

The conformation and its relaxation of a single polymer depend on solvent quality in a polymer solution: a polymer collapses into a globule in a poor solvent, while the polymer swells in a good solvent. When one translocates a polymer through a narrow pore, a drastic conformational change occurs such that the kinetics of the translocation is expected to depend on the solvent quality. However, the effects of solvent quality on the translocation kinetics have been controversial. In this study, we employ a coarse-grained model for a polymer and perform Langevin dynamics simulations for the driven translocation of a polymer in various types of solvents. We estimate the free energy of polymer translocation using steered molecular dynamics simulations and Jarzynski's equality and find that the free energy barrier for the translocation increases as the solvent quality becomes poorer. The conformational entropy contributes most to the free energy barrier of the translocation in a good solvent, while a balance between entropy and energy matters in a poor solvent. Interestingly, contrary to what is expected from the free energy profile, the translocation kinetics is a non-monotonic function of the solvent quality. We find that for any type of solvent, the polymer conformation stays far away from the equilibrium conformation during translocation due to an external force and tension propagation. However, the degree of tension propagation differs depending on the solvent quality as well as the magnitude of the external force: the tension propagation is more significant in a good solvent than in a poor solvent. We illustrate that such differences in tension propagation and non-equilibrium conformations between good and poor solvents are responsible for the complicated non-monotonic effects of solvent quality on the translocation kinetics.

Simulation study on the translocation of polyelectrolyte through conical nanopores

Experiments have suggested that the conical nanopore may be a reasonable sensor for the biopolymer analysis as it can provide high-resolution current signal. In this paper, we use Langevin dynamics simulation to study the translocation of charged polymer (polyelectrolyte) through three different conical nanopores, a single-conical nanopore with large entry and small exit (pore I), a single-conical nanopore with small entry and large exit (pore II), and a double-conical nanopore with the tip (narrowest place) at the middle (pore III). Simulation shows that the detailed translocation behaviors are of pore structure dependence. Pore I might be the most reasonable one for the polyelectrolyte analysis, especially at strong monomer-pore attraction, since it can efficiently reduce the polyelectrolyte speed at the tip. The simulation results are interpreted by the free energy profiles of the polyelectrolyte translocation through different pores and the time of individual monomer passing through the tips.

Theoretical study on the polymer translocation into an attractive sphere

We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R^* has a scaling relation with the polymer length N as R^* ∼ N^β. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.

Temperature dependence of the translocation time of polymer through repulsive nanopores

The forced translocation of a polymer chain through repulsive nanopores was studied by using Langevin dynamics simulations. The polymer is in the compact globule state at low temperature and in the random coil state at high temperature. Simulation results show that the mean translocation time 〈τ〉 is highly dependent on the temperature T and the minimal 〈τ〉 is located near the coil-globule transition temperature. Moreover, the scaling behaviors 〈τ〉 ∼ N^α and 〈τ〉 ∼ F^-δ are studied, with N the polymer length and F the driving force inside the nanopore. Universal values α = 1.4 and δ = 0.85 are observed for the polymer in the random coil state. While for the polymer in the compact globule state, α decreases from α = 2 at weak driving to 1.2 at strong driving for short N and δ increases with decreasing T in the low F region, but we find universal exponents α = 1.6 for long N and δ = 0.85 in the large F region. Results show that polymer's conformation plays a much more important role than the diffusion coefficient in controlling the translocation time of the polymer chain.

Stochastic resonance during a polymer translocation process

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Polymer translocation through nanopore into active bath

Polymer translocation through nanopores into a crowded environment is of ubiquitous importance in many biological processes. Here we investigate polymer translocation through a nanopore into an active bath of self-propelled particles in two-dimensional space using Langevin dynamics simulations. Interestingly, we find that the mean translocation time τ can show a bell-shape dependence on the particle activity F_a at a fixed volume fraction ϕ, indicating that the translocation process may become slower for small activity compared to the case of the passive media, and only when the particle activity becomes large enough can the translocation process be accelerated. In addition, we also find that τ can show a minimum as a function of ϕ if the particle activity is large enough, implying that an intermediate volume fraction of active particles is most favorable for the polymer translocation. Detailed analysis reveals that such nontrivial behaviors result from the two-fold effect of active bath: one that active particles tend to accumulate near the pore, providing an extra pressure hindering the translocation, and the other that they also aggregate along the polymer chain, generating an effective pulling force accelerating the translocation. Such results demonstrate that active bath plays rather subtle roles on the polymer translocation process.

Ratchet rectification effect on the translocation of a flexible polyelectrolyte chain

We report a three dimensional Langevin dynamics simulation of a uniformly charged flexible polyelectrolyte chain, translocating through an asymmetric narrow channel with periodically varying cross sections under the influence of a periodic external electric field. When reflection symmetry of the channel is broken, a rectification effect is observed with a favored direction for the chain translocation. For a given volume of the channel unit and polymer length, the rectification occurs below a threshold frequency of the external periodic driving force. We have also observed that the extent of the rectification varies non-monotonically with increasing molecular weight and the strength of geometric asymmetry of the channel. Observed non-monotonicity of the rectification performance has been interpreted in terms of a competition between two effects arising from the channel asymmetry and change in conformational entropy. An analytical model is presented with predictions consistent with the simulation results.

Simulation on the translocation of homopolymers through sandwich-like compound channels

The forced translocation of homopolymers through αβα sandwich-like compound channels was investigated by Monte Carlo simulation. The interaction between polymer and part α is strongly attractive, whereas that between polymer and part β is purely repulsive. Simulation results show that the translocation is influenced obviously by the length of part β (Lβ) and the starting position of part β (Lα1). For small Lβ, the translocation is mainly governed by the escaping process, and polymer is trapped near the exit of the channel. However, the translocation time can be tuned by varying Lα1 and the fastest translocation can be achieved at relatively large Lα1. Whereas for large Lβ and small Lα1, the translocation is mainly controlled by the filling process. It is difficult for polymer to enter the channel, and polymer is trapped at the first αβ interface. Finally, the dynamics for the filling process and the escaping process are discussed from the view of free-energy landscape, respectively.

Translocation of polymers into crowded media with dynamic attractive nanoparticles

The translocation of polymers through a small pore into crowded media with dynamic attractive nanoparticles is simulated. Results show that the nanoparticles at the trans side can affect the translocation by influencing the free-energy landscape and the diffusion of polymers. Thus the translocation time τ is dependent on the polymer-nanoparticle attraction strength ɛ and the mobility of nanoparticles V. We observe a power-law relation of τ with V, but the exponent is dependent on ɛ and nanoparticle concentration. In addition, we find that the effect of attractive dynamic nanoparticles on the dynamics of polymers is dependent on the time scale. At a short time scale, subnormal diffusion is observed at strong attraction and the diffusion is slowed down by the dynamic nanoparticles. However, the diffusion of polymers is normal at a long time scale and the diffusion constant increases with the increase in V.

Langevin dynamics simulation on the translocation of polymer through α-hemolysin pore

The forced translocation of a polymer through an α-hemolysin pore under an electrical field is studied using a Langevin dynamics simulation. The α-hemolysin pore is modelled as a connection of a spherical vestibule and a cylindrical β-barrel and polymer-pore attraction is taken into account. The results show that polymer-pore attraction can help the polymer enter the vestibule and the β-barrel as well; however, a strong attraction will slow down the translocation of the polymer through the β-barrel. The mean translocation time for the polymer to thread through the β-barrel increases linearly with the polymer length. By comparing our results with that of a simple pore without a vestibule, we find that the vestibule helps the polymer enter and thread through the β-barrel. Moreover, we find that it is easier for the polymer to thread through the β-barrel if the polymer is located closer to the surface of the vestibule. Some simulation results are explained qualitatively by theoretically analyzing the free-energy landscape of polymer translocation.

Nonmonotonic diffusion of particles among larger attractive crowding spheres

We study the diffusive motion of particles among fixed spherical crowders. The diffusers interact with the crowders through a combination of a hard-core repulsion and a short-range attraction. The long-time effective diffusion coefficient of the diffusers is found to depend nonmonotonically on the strength of their attraction to the crowders. That is, for a given concentration of crowders, a weak attraction to the crowders enhances diffusion. We show that this counterintuitive fact can be understood in terms of the mesoscopic excess chemical potential landscape experienced by the diffuser. The roughness of this excess chemical potential landscape quantitatively captures the nonmonotonic dependence of the diffusion rate on the strength of crowder-diffuser attraction; thus, it is a purely static predictor of dynamic behavior. The mesoscopic view given here provides a unified explanation for enhanced diffusion effects that have been found in various systems of technological and biological interest.

Study on the polymer translocation induced blockade ionic current inside a nanopore by Langevin dynamics simulation

The blockade ionic current inside a nanopore due to polymer translocation is studied using a three-dimensional Langevin dynamics method. The blockade current IB is dependent on the polymer length N, polymer configuration, polymer-pore interaction, and charge of the polymer. The behavior of IB can be explained using four factors: (1) the volume vacancy fraction fV inside the pore; (2) the conformation of the polymer; (3) the location of the polymer inside the pore; and (4) the total charge Ztot inside the pore. We find that IB increases with fV but decreases with increasing |Ztot|. The influence of the polymer's conformation is complex, dependent on the size of polymer RG and the cross-sectional size of the pore s. A compact conformation can decrease IB when RG > s but increase IB when RG < s. For the latter case, the conformation of the polymer is too small to block the pore, thus providing a broad passage for the ions. At the same fV, monomers will locate close to the surface with a large polymer-pore attraction, which also provides a large IB.

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.

Influence of polymer-pore interaction on the translocation of a polymer through a nanopore

The translocation of a bond fluctuation polymer through an interacting nanopore is studied using dynamic Monte Carlo simulation. A driving force F is applied only for monomers inside the pore. The influence of polymer-pore interaction on the scaling relation τ~N(α) is studied for both unbiased and biased translocations, with τ the translocation time and N the polymer length. Results show that the exponent α is dependent on the polymer-pore interaction. For a noninteracting pore, we find α=2.48 for unbiased translocation and α=1.35 for strong biased translocation; for strong attraction, we find α=2.35 for unbiased translocation and α=1.22 for strong biased translocation. The unbiased translocation corresponds to the low-NF regime whereas the strong biased translocation corresponds to the high-NF regime.

Effects of an attractive wall on the translocation of polymer under driving

The effects of an attractive wall at the trans side on the translocation of an eight-site bond-fluctuation model (BFM) polymer through a pore in a membrane under driving are simulated by the dynamic Monte Carlo method. The attractive wall shows two contrary effects: its excluded volume effect reduces configuration entropy and thus hinders the translocation of the polymer, while its attraction decreases the energy and thus accelerates the translocation. At a critical polymer-wall interaction ε* ≈- 1, we find that the two effects compensate each other and the translocation time τ is roughly independent of the separation distance between the wall and the pore. The value ε* ≈- 1 is roughly equal to the critical adsorption point for the BFM polymer. Moreover, the value of the critical attraction is roughly independent of chain length N and chemical potential difference Δμ. At last, a scaling relation τ ∼ N(α) is observed for polymer translocation at a high value of NΔμ. Though the translocation time is highly dependent on the polymer-wall interaction and pore-wall separation distance, the exponent α is always about 1.30 ± 0.05 so long as NΔμ is large enough.

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 properties of copolymer (A(n)B(m))(l) through an interacting pore

The translocation of a copolymer (A(n)B(m))(l) through an interacting pore was investigated by Monte Carlo simulation on a three-dimensional cubic lattice. Interactions between monomer A and pore ɛ(A) and between monomer B and pore ɛ(B) were considered. The difference between two translocation orientations, orientation A with monomer A entering the pore first and orientation B with monomer B first, was studied. Both the orientation probability and translocation time are dependent on monomer-pore interactions, block length, and fractions of monomers. The separation of different copolymers using translocation was also discussed. The results were explained qualitatively from the view of the free energy landscape of the copolymer translocation.

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 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.

Translocation dynamics with attractive nanopore-polymer interactions

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