Polymer translocation: The effect of backflow

Protocols for translocation processes of flexible polymers through a pore using LAMMPS

Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is an open-source, powerful simulator with a customizable platform for extensive Langevin dynamics simulations. Here, we present a protocol for using LAMMPS to develop coarse-grained models of polymeric systems with macromolecular crowding, an integral part of any soft matter or biophysical system. We describe steps for installing software, using LAMMPS basic commands and code, and translocating polymers. This protocol has potential applications in developing mathematical models for DNA sequencing, controlled drug delivery, and cellular transport processes. For complete details on the use and execution of this protocol, please refer to Garg et al.1.

The journey of a single polymer chain to a nanopore

For a polymer to successfully thread through a nanopore, it must first find the nanopore. This so-called capture process is typically considered as a two-stage operation consisting of the chain being delivered at the entrance of the nanopore and then insertion of one of the ends. Studying molecular dynamics-lattice Boltzmann simulations of the capture of a single polymer chain under pressure driven hydrodynamic flow, we observe that the insertion can be essentially automatic with no delay for the ends searching for the nanopore. The deformation of the chain within the converging flow area and also, the interplay between the chain elastic forces and the hydrodynamic drag play an important role in the capture of the chain by the nanopore. Along the journey to the nanopore, the chain may form folded shapes. The competition between the elastic and hydrodynamic forces results in unraveling of the folded conformations (hairpins) as the chain approaches the nanopore. Although the ends are not the only monomers that can thread into the nanopore, the unraveling process can result in much higher probability of threading by the ends.

Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore

The advent of solid state nanodevices allows for interrogating the physicochemical properties of a polyelectrolyte chain by electrophoretically driving it through a nanopore. Salient dynamical aspects of the translocation process have been recently characterized by theoretical and computational studies of model polymer chains free from self-entanglement. However, sufficiently long equilibrated chains are necessarily knotted. The impact of such topological "defects" on the translocation process is largely unexplored, and is addressed in this Letter. By using Brownian dynamics simulations on a coarse-grained polyelectrolyte model we show that knots, despite being trapped at the pore entrance, do not per se cause the translocation process to jam. Rather, knots introduce an effective friction that increases with the applied force, and practically halts the translocation above a threshold force. The predicted dynamical crossover, which is experimentally verifiable, ought to be relevant in applicative contexts, such as DNA nanopore sequencing.

SCREW MOTION OF DNA DUPLEX DURING TRANSLOCATION THROUGH PORE I: INTRODUCTION OF THE COARSE-GRAINED MODEL

Based upon the structural properties of DNA duplexes and their counterion-water surrounding in solution, we have introduced here a screw model which may describe translocation of DNA duplexes through artificial nanopores of the proper diameter (where the DNA counterion–hydration shell can be intact) in a qualitatively correct way. This model represents DNA as a kind of "screw," whereas the counterion-hydration shell is a kind of "nut." Mathematical conditions for stable dynamics of the DNA screw model are investigated in detail. When an electrical potential is applied across an artificial membrane with a nanopore, the "screw" and "nut" begin to move with respect to each other, so that their mutual rotation is coupled with their mutual translation. As a result, there are peaks of electrical current connected with the mutual translocation of DNA and its counterion–hydration shell, if DNA is possessed of some non-regular base-pair sequence. The calculated peaks of current strongly resemble those observed in the pertinent experiments. An analogous model could in principle be applied to DNA translocation in natural DNA–protein complexes of biological interest, where the role of "nut" would be played by protein-tailored "channels." In such cases, the DNA screw model is capable of qualitatively explaining chemical-to-mechanical energy conversion in DNA–protein molecular machines via symmetry breaking in DNA–protein friction.

Fluid-solid boundary conditions for multiparticle collision dynamics

The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.

Unforced polymer translocation compared to the forced case

We present results for unforced polymer translocation from simulations using Langevin dynamics in two dimensions (2D) to four dimensions and stochastic rotation dynamics supporting hydrodynamic modes in three dimensions (3D). We compare our results to forced translocation and a simplified model where the polymer escapes from an infinite pore. The simple model shows that the scaling behavior of unforced translocation is independent of the dimension of the side to which the polymer is translocating. We find that, unlike its forced counterpart, unforced translocation dynamics is insensitive to pore design. Hydrodynamics is seen to markedly speed up the unforced translocation process but not to affect the scaling relations. Average mean-squared displacement shows scaling with average transition time in unforced but not in forced translocation. The waiting-time distribution in unforced translocation follows closely Poissonian distribution. Our measured transfer probabilities align well with those obtained from an equilibrium theory in 3D, but somewhat worse in 2D, where a polymer's relaxation toward equilibrium with respect to its translocation time is slower. Consequently, in stark contrast to forced translocation, unforced translocation is seen to remain close to equilibrium and shows clear universality.

Nondriven polymer translocation through a nanopore: computational evidence that the escape and relaxation processes are coupled

Most of the theoretical models describing the translocation of a polymer chain through a nanopore use the hypothesis that the polymer is always relaxed during the complete process. In other words, models generally assume that the characteristic relaxation time of the chain is small enough compared to the translocation time that nonequilibrium molecular conformations can be ignored. In this paper, we use molecular dynamics simulations to directly test this hypothesis by looking at the escape time of unbiased polymer chains starting with different initial conditions. We find that the translocation process is not quite in equilibrium for the systems studied, even though the translocation time tau is about 10 times larger than the relaxation time tau{r}. Our most striking result is the observation that the last half of the chain escapes in less than approximately 12% of the total escape time, which implies that there is a large acceleration of the chain at the end of its escape from the channel.

Critical evaluation of the computational methods used in the forced polymer translocation

In forced polymer translocation, the average translocation time tau scales with respect to pore force f and polymer length N as tau approximately f;{-1}N;{beta} . We demonstrate that an artifact in the Metropolis Monte Carlo method resulting in breakage of the force scaling with large f may be responsible for some of the controversies between different computationally obtained results and also between computational and experimental results. Using Langevin dynamics simulations we show that the scaling exponent beta<or=1+nu is not universal, but depends on f . Moreover, we show that forced translocation can be described by a relatively simple force balance argument and beta to arise solely from the initial polymer configuration.

Ejection dynamics of polymeric chains from viral capsids: effect of solvent quality

We present simulations investigating the effects of solvent quality on the dynamics of flexible (RNA-like) and semiflexible (DNA-like) polymers ejecting from spherical viral capsids. We find that the mean ejection time increases and the ejection time distributions are broadened as the solvent quality decreases. Our results thus suggest that DNA ejection may be very efficiently controlled by tuning the salt concentration in the environment, in agreement with recent experimental findings. We also observe random pauses in the ejection. These become extremely long for semiflexible polymers at lower solvent quality, and we interpret this as a signature of a low driving force for ejection. We find that, for most polymers, ejection is an all-or-nothing process at the solvent conditions we investigated: polymers normally completely eject once the process is initiated.

Molecular Dynamics simulation of a polymer chain translocating through a nanoscopic pore: hydrodynamic interactions versus pore radius

The detection of linear polymers translocating through a nanoscopic pore is a promising idea for the development of new DNA analysis techniques. However, the physics of constrained macromolecules and the fluid that surrounds them at the nanoscopic scale is still not well understood. In fact, many theoretical models of polymer translocation neglect both excluded-volume and hydrodynamic effects. We use Molecular Dynamics simulations with explicit solvent to study the impact of hydrodynamic interactions on the translocation time of a polymer. The translocation time tau that we examine is the unbiased (no charge on the chain and no driving force) escape time of a polymer that is initially placed halfway through a pore perforated in a monolayer wall. In particular, we look at the effect of increasing the pore radius when only a small number of fluid particles can be located in the pore as the polymer undergoes translocation, and we compare our results to the theoretical predictions of Chuang et al. (Phys. Rev. E 65, 011802 (2001)). We observe that the scaling of the translocation time varies from tau approximately N 11/5 to tau approximately N 9/5 as the pore size increases (N is the number of monomers that goes up to 31 monomers). However, the scaling of the polymer relaxation time remains consistent with the 9/5 power law for all pore radii.

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.

Polymer capture by electro-osmotic flow of oppositely charged nanopores

The authors have addressed theoretically the hydrodynamic effect on the translocation of DNA through nanopores. They consider the cases of nanopore surface charge being opposite to the charge of the translocating polymer. The authors show that, because of the high electric field across the nanopore in DNA translocation experiments, electro-osmotic flow is able to create an absorbing region comparable to the size of the polymer around the nanopore. Within this capturing region, the velocity gradient of the fluid flow is high enough for the polymer to undergo coil-stretch transition. The stretched conformation reduces the entropic barrier of translocation. The diffusion limited translocation rate is found to be proportional to the applied voltage. In the authors' theory, many experimental variables (electric field, surface potential, pore radius, dielectric constant, temperature, and salt concentration) appear through a single universal parameter. They have made quantitative predictions on the size of the adsorption region near the pore for the polymer and on the rate of translocation.