Driven polymer translocation in good and bad solvent: Effects of hydrodynamics and tension propagation

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.

Delayed collapse transitions in a pinned polymer system

Employing Langevin dynamics simulations, we investigated the kinetics of the collapse transition for a polymer of length N when a particular monomer at a position 1≤X≤N is pinned. The results are compared with the kinetics of a free polymer. The equilibrium θ-point separating the coil from the globule phase is located by a crossover in 〈R_{g}^{2}〉/N plots of different chain lengths. Our simulation supports a three-stage mechanism for free and pinned polymer collapse: the formation of pearls, the coarsening of pearls, and the formation of a compact globule. Pinning the central monomer has negligible effects on the kinetics as it does not break the symmetry. However, pinning a monomer elsewhere causes the process to be delayed by a constant factor ϕ_{X} depending linearly upon X. The total collapse time scales with N as τ_{c}∼ϕ_{X}N^{1.60±0.03}, which implies τ_{c} is maximum when an end monomer is pinned (X=1 or N), while when pinning the central monomer (X=N/2) it is minimum and identical to that of a free polymer. The average cluster size N_{c}(t) grows in time as t^{z}, where z=1.00±0.04 for a free particle, whereas we identify two time regimes separated by a plateau for pinned polymers. At longer times, z=1.00±0.04, while it deviates in early time regimes significantly, depending on the value of X.

The breakdown of the local thermal equilibrium approximation for a polymer chain during packaging

The conformational relaxation of a polymer chain often slows down in various biological and engineering processes. The polymer, then, may stay in nonequilibrium states throughout the process such that one may not invoke the local thermal equilibrium (LTE) approximation, which has been usually employed to describe the kinetics of various processes. In this work, motivated by recent single-molecule experiments on DNA packaging into a viral capsid, we investigate how the nonequilibrium conformations and the LTE approximation would affect the packaging of a polymer chain into small confinement. We employ a simple but generic coarse-grained model and Langevin dynamics simulations to investigate the packaging kinetics. The polymer segments (both inside and outside the confinement) stay away from equilibrium under strong external force. We devise a simulation scheme to invoke the LTE approximation during packaging and find that the relaxation of nonequilibrium conformations plays a critical role in regulating the packaging rate.

Translocation of Star Polyelectrolytes through a Nanopore

The electric field driven translocation of charged star polymers through a cylindrical nanopore has been studied using dissipative particle dynamics simulations. The critical field strength required to induce translocation depends on both the number of arms and the number of beads per arm. It may therefore be possible to separate star polyelectrolytes of different arm lengths using electric field driven translocation through a nanopore. The average translocation time exhibits nonmonotonic variation with the number of arms for good solvent conditions. During translocation, a star polymer with many arms is stretched along the pore axis to a lesser extent as compared to its linear counterpart. Unlike a linear chain that shows tension propagation with large tensions for bonds about to enter the pore, a star has the tensest bonds closest to the branch point whose connectivity to multiple arms raises difficulty for its entry and passage.

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.

Dynamics of driven translocation of semiflexible polymers

We study translocation of semiflexible polymers driven by force f_{d} inside a nanometer-scale pore using our three-dimensional Langevin dynamics model. We show that the translocation time τ increases with increasing bending rigidity κ. Similarly, the exponent β for the scaling of τ with polymer length N,τ∼N^{β}, increases with increasing κ as well as with increasing f_{d}. By comparing waiting times between semiflexible and fully flexible polymers we show that for realistic f_{d} translocation dynamics is to a large extent, but not completely, determined by the polymer's elastic length measured in number of Kuhn segments N_{Kuhn}. Unlike in driven translocation of flexible polymers, friction related to the polymer segment on the trans side has a considerable effect on the resulting dynamics. This friction is intermittently reduced by buckling of the polymer segment in the vicinity of the pore opening on the trans side. We show that in the experimentally relevant regime where viscosity is higher than in computer simulation models, the probability for this buckling increases with increasing f_{d}, giving rise to a larger contribution to the trans side friction at small f_{d}. Similarly to flexible polymers, we find significant center-of-mass diffusion of the cis side polymer segment which speeds up translocation. This effect is larger for smaller f_{d}. However, this speedup is smaller than the slowing down due to the trans side friction. At large enough N_{Kuhn}, the roles can be seen to be reversed, and the dynamics of flexible polymers can be reached. However, for example, polymers used in translocation experiments of DNA are elastically so short that the finite-length dynamics outlined here applies.

Granular chain escape from a pore in a wall in the presence of particles on one side: a comparison to polymer translocation

Escape of a granular chain from a pore in a wall in the presence of diffusing granular particles on one side of the wall is studied experimentally. The escape time shows power-law behavior as a function of the chain length (τ ∝ Nα). A Langevin dynamics simulation of a polymer chain in a similar geometry is also performed and similar results to those for a granular system are obtained. A simple scaling argument and an energetic argument (based on the Onsager principle) are introduced which explain our results very well. Experiments (simulations) show that by increasing the number of particles on one side of the wall from zero, the exponent α decreases from 2.6 ± 0.1 (3.1 ± 0.1) to about 2. Both scaling and the Onsager principle argument predict α = 2 at high particle concentration, in agreement with the experiments and simulations. In the absence of particles, the scaling predicts τ = N2.5 (in agreement with the experimental result for the granular chain) and the Onsager principle predictsτ = N3 ln N, supporting the simulation result for the polymer chain. Experiments, simulations, scaling, and the Onsager principle confirm an inverse relation between τ and the density of particles on one side of the wall.

Quantification of tension to explain bias dependence of driven polymer translocation dynamics

Motivated by identifying the origin of the bias dependence of tension propagation, we investigate methods for measuring tension propagation quantitatively in computer simulations of driven polymer translocation. Here, the motion of flexible polymer chains through a narrow pore is simulated using Langevin dynamics. We measure tension forces, bead velocities, bead distances, and bond angles along the polymer at all stages of translocation with unprecedented precision. Measurements are done at a standard temperature used in simulations and at zero temperature to pin down the effect of fluctuations. The measured quantities were found to give qualitatively similar characteristics, but the bias dependence could be determined only using tension force. We find that in the scaling relation τ∼N^{β}f_{d}^{α} for translocation time τ, the polymer length N, and the bias force f_{d}, the increase of the exponent β with bias is caused by center-of-mass diffusion of the polymer toward the pore on the cis side. We find that this diffusion also causes the exponent α to deviate from the ideal value -1. The bias dependence of β was found to result from combination of diffusion and pore friction and so be relevant for polymers that are too short to be considered asymptotically long. The effect is relevant in experiments all of which are made using polymers whose lengths are far below the asymptotic limit. Thereby, our results also corroborate the theoretical prediction by Sakaue's theory [Polymers 8, 424 (2016)2073-436010.3390/polym8120424] that there should not be bias dependence of β for asymptotically long polymers. By excluding fluctuations we also show that monomer crowding at the pore exit cannot have a measurable effect on translocation dynamics under realistic conditions.

Interstitial micelles in binary blends of ABA triblock copolymers and homopolymers

We investigate triblock-homopolymer blends of types A1BA2/A and A1BA2/B, using a lattice Monte Carlo method. While the simulated triblock chains are compositionally symmetric in terms of the A-to-B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt and the A1BA2 solutions in selective solvent the phase behavior is relatively well known, including existence and stability of the interstitial micelles which were discovered in previous Monte Carlo simulations. In this paper we study the stability of the interstitial micelles as a function of triblock volume fraction in selective homopolymers of either type A or type B, using two significantly different homopolymer chain lengths. We found that adding selective homopolymer of type A shifts the stability of the interstitial micelles into significantly higher temperatures. We also obtained, via self-assembly, intriguing new nanostructures which can be identified as ordered truncated octahedra. Finally, we established that the phase behavior of the triblock-homopolymer blends depends relatively weakly on the chain length of the added homopolymer.

Uniform description of polymer ejection dynamics from capsid with and without hydrodynamics

We use stochastic rotation dynamics (SRD) to examine the dynamics of the ejection of an initially strongly confined flexible polymer from a spherical capsid with and without hydrodynamics. The results obtained using stochastic rotation dynamics (SRD) are compared to similar Langevin simulations. Inclusion of hydrodynamic modes speeds up the ejection but also allows the part of the polymer outside the capsid to expand closer to equilibrium. This shows as higher values of radius of gyration when hydrodynamics are enabled. By examining the waiting times of individual polymer beads, we find that the waiting time t_{w} grows with the number of ejected monomers s as a sum of two exponents. When ≈63% of the polymer has ejected, the ejection enters the regime of slower dynamics. The functional form of t_{w} versus s is universal for all ejection processes starting from the same initial monomer densities. Inclusion of hydrodynamics only reduces its magnitude. Consequently, we define a universal scaling function h such that the cumulative waiting time t=N_{0}h(s/N_{0}) for large N_{0}. Our unprecedentedly precise measurements of force indicate that this form for t_{w}(s) originates from the corresponding force toward the pore decreasing superexponentially at the end of the ejection. Our measured t_{w}(s) explains the apparent superlinear scaling of the ejection time with the polymer length for short polymers. However, for asymptotically long polymers, t_{w}(s) predicts linear scaling.