Polymer translocation through pores with complex geometries

Polymer translocation: Effects of confinement

We investigate the influence of varying confinement on the dynamics of polymer translocation through a cone-shaped channel. For this, a linear polymer chain is modeled using self-avoiding walks on a square lattice. The cis side of a cone-shaped channel has a finite volume, while the trans side has a semi-infinite space. The confining environment is varied either by changing the position of the back wall while keeping the apex angle fixed or altering the apex angle while keeping the position of the back wall fixed. In both cases, the effective space ϕ, which represents the number of monomers in a chain relative to the total number of accessible sites within the cone, is reduced due to the imposed confinement. Consequently, the translocation dynamics are affected. We analyze the entropy of the confined system as a function of ϕ, which exhibits nonmonotonic behavior. We also calculate the free energy associated with the confinement as a function of a virtual coordinate for different positions of the back wall (base of the cone) along the conical axis for various apex angles. Employing the Fokker-Planck equation, we calculate the translocation time as a function of ϕ for different solvent conditions across the channel. Our findings indicate that the translocation time decreases as ϕ increases, but it eventually reaches a saturation point at a certain value of ϕ. Moreover, we highlight the possibility of controlling the translocation dynamics by manipulating the solvent quality across the channel. Furthermore, our investigation delves into the intricacies of polymer translocation through a cone-shaped channel, considering both repulsive and neutral interactions with the channel wall. This exploration unveils nuanced dynamics and sheds light on the factors that significantly impact translocation within confined channels.

Constraints on Knot Insertion, Not Internal Jamming, Control Polycatenane Translocation Dynamics through Crystalline Pores

The translocation of polymers through pores and channels is an archetypal process in biology and is widely studied and exploited for applications in bio- and nanotechnology. In recent times, the translocation of polymers of various different topologies has been studied both experimentally and by computer simulation. However, in some cases, a clear understanding of the precise mechanisms that drive their translocation dynamics can be challenging to derive. Experimental methods are able to provide statistical details of polymer translocation, but computer simulations are uniquely placed to uncover a finer level of mechanistic understanding. In this work, we use high-throughput molecular simulations to reveal the importance that knot insertion rates play in controlling translocation dynamics in the small pore limit, where unexpected nonpower law behavior emerges. This work both provides new predictive understanding of polycatenane translocation and shows the importance of carefully considering the role of the definition of translocation itself.

Simulation Study of Chain-like Body Translocation through Conical Pores in Thick Membranes

Artificial membranes with conical pores and controllable thickness reveal ionic-transport capabilities that are superior compared with those offered by cylindrical pores. By simulating the translocation of an abstract chain-like body through a conical pore in a membrane with a variable thickness, we formulate a statistical model of the translocation time τ. Our rough model encodes the biochemical details of a given real chain-like molecule as evolving sequences of the allowed chain-like body’s conformations. In our simulation experiments, we focus primarily on pore geometry and kinetic aspects of the translocation process. We study the impact of the membrane thickness L, and both conical-pore diameters ϕcis,ϕtrans on the probability distribution of τ. We have found that for all considered simulation setups, the randomness of τ is accurately described by the family of Moyal distributions while its expected value τ is proportional to Lξ, with ξ being dependent on ϕcis,ϕtrans.

Evaluating the applicability of the Fokker-Planck equation in polymer translocation: a Brownian dynamics study

Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N = 21-61. The rate of translocation is controlled by a tunable friction coefficient, γ0p, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length as <τ1> ∼ (N - Np)(α), where Np is the average number of monomers in the nanopore. The exponent approaches the value α = 2 when the pore friction is sufficiently high, in accord with the prediction for the case of the quasi-static regime where pore friction dominates. In the case of forced translocation, the polymer chain is stretched and compressed on the cis and trans sides, respectively, for low γ0p. However, the chain approaches conformational quasi-equilibrium for sufficiently large γ0p. In this limit the observed scaling of <τ1> with driving force and chain length supports the Fokker-Planck (FP) prediction that <τ> ∝ N/fd for sufficiently strong driving force. Monte Carlo simulations are used to calculate translocation free energy functions for the system. The free energies are used with the FP equation to calculate translocation time distributions. At sufficiently high γ0p, the predicted distributions are in excellent agreement with those calculated from the BD simulations. Thus, the FP equation provides a valid description of translocation dynamics for sufficiently high pore friction for the range of polymer lengths considered here. Increasing N will require a corresponding increase in pore friction to maintain the validity of the FP approach. Outside the regime of low N and high pore friction, the polymer is out of equilibrium, and the FP approach is not valid.

Polymer translocation dynamics in the quasi-static limit

Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to <τ> ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.

Through the eye of the needle: recent advances in understanding biopolymer translocation

In recent years polymer translocation, i.e., transport of polymeric molecules through nanometer-sized pores and channels embedded in membranes, has witnessed strong advances. It is now possible to observe single-molecule polymer dynamics during the motion through channels with unprecedented spatial and temporal resolution. These striking experimental studies have stimulated many theoretical developments. In this short theory-experiment review, we discuss recent progress in this field with a strong focus on non-equilibrium aspects of polymer dynamics during the translocation process.

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.

Force-driven polymer translocation through a nanopore: an old problem revisited

We consider DNA translocation through a pore in a planar membrane. The pore is so narrow that only one DNA segment can fit in. Assuming that the biasing force f acts inside the pore only, and that the DNA monomer number N is asymptotically large, we modify the previously developed treatment of the stretched part of the pre-translocated polymer by introducing the concept of "iso-flux trumpet". We show that friction of a moving chain in the trumpet, although it determines the speed of the process, provides only a marginal fraction of overall dissipation in the process. The dominant dissipation turns out to be due to irreversible entropic squeezing of the chain into the small pore. We also discover that because of the role of the membrane a much larger amount of heat of order k(B)T per monomer gets transferred from the heat bath on the post-translocation side to that on the pre-translocation side.

Single-polymer dynamics under constraints: scaling theory and computer experiment

The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces--a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.