We study the dynamics of a knot in a semiflexible polymer confined to a narrow channel of width comparable to the polymers' persistence length. Using a combination of Brownian dynamics simulations and a coarse-grained stochastic model, we characterize the coupled dynamics of knot size variation and knot diffusion along the polymer, which ultimately leads to spontaneous unknotting. We find that the knot grows to macroscopic size before disappearing. Interestingly, an external force applied to the ends of the confined polymer speeds up spontaneous unknotting.
We investigate the ejection dynamics of a ring polymer out of a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. The ejection dynamics for ring polymers shows two regimes like for linear polymers, depending on the relative length of the chain compared with the channel. For long chains with length $N$ larger than the critical chain length $N_{c}$, at which the chain just fully occupies the nanochannel, the ejection for ring polymers is faster compared with linear chains of identical length due to a larger entropic pulling force; while …
We investigate the chain conformation of ring polymers confined to a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. We predict that the longitudinal size of a ring polymer scales with the chain length and the diameter of the channel in the same manner as that for linear chains based on scaling analysis and Flory-type theory. Moreover, Flory-type theory also gives the ratio of the longitudinal sizes for a ring polymer and a linear chain with identical chain length. These theoretical predictions are confirmed by numerical simulations.…
Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation through a nanochannel embedded in two dimensions under an applied external field. We examine the translocation time for various ratio of the channel length $L$ to the polymer length $N$. For short channels $L\ll N$, the translocation time $τ\sim N^{1+ν}$ under weak driving force $F$, while $τ\sim F^{-1}L$ for long channels $L\gg N$, independent of the chain length $N$. Moreover, we observe a minimum of translocation time as a function of $L/N$ for different driving forces and cha…
We examine pressure-driven non-equilibrium transport of linear, circular and star polymers through a nanochannel containing a rectangular pit with full hydrodynamic interactions and thermal fluctuations. We demonstrate that with sufficiently small pressure differences, there is contour length-dependent entropic trapping of the polymer in the pit when the pit and the polymer sizes are compatible. This is due to competition between flow and chain relaxation in the pit, which leads to a non-monotonic dependence of the polymer mobility on its size and should aid in the design of nanofiltration dev…
Polymer materials with low water uptake exhibit a highly heterogeneous interior, characterized by water clusters in the form of nanodroplets and nanochannels. Here, based on our recent insights from computer simulations, we argue that water cluster structure has large implications for ionic transport and selective permeability in polymer membranes. Importantly, we demonstrate that the two key quantities for transport, the ion diffusion and the solvation free energy inside the polymer, are extremely sensitive to molecular details of the water clusters. In particular, we highlight the significan…
We expand the blob theory for freely-jointed chains and perform molecular dynamics simulations to study the behavior of polymers confined in cylindrical channels. From weak to strong confinement, five scaling regimes, de Gennes, extended de Gennes, transition, backfolding, and Odijk regimes, are distinguished for neutral polymers.The size scalings in each regime are derived as a function of the channel width. The scaling exponents $-1$ and $-1/3$ are obtained for the transition and backfolding regimes, respectively, which result from the reduction of the excluded volume of the segments by rest…
We consider the flow-driven translocation of single polymer chains through nanochannels. Using analytical calculations based on the de Gennes blob model and mesoscopic numerical simulations, we estimate the threshold flux for the translocation of chains of different number of monomers. The translocation of the chains is controlled by the competition between entropic and hydrodynamic effects, which set a critical penetration length for the chain before it can translocate through the channel. We demonstrate that the polymers show two different translocation regimes depending on how their length …
Monte Carlo simulations are used to study the conformational properties of a folded semiflexible polymer confined to a long channel. We measure the variation in the conformational free energy with respect to the end-to-end distance of the polymer, and from these functions we extract the free energy of the hairpin fold, as well as the entropic force arising from interactions between the portions of the polymer that overlap along the channel. We consider the scaling of the free energies with respect to varying the persistence length of the polymer, as well as the channel dimensions for confineme…
Trapping macromolecules in nanopits finds multifarious applications in polymer separation, filtering biomolecules etc. However, tuning the locomotion of polymers in channels of nanoscopic dimensions is greatly restricted by the comparative advective and diffusive components of velocities. Using the polymer affinity toward the solvent and the wall, and the polymer structure, a mechanism is proposed to induce selective trapping of polymers. Similar to fractional distillation of hydrocarbons based on molecular weight, a technique of fractional segregation, depending on the channel wettability of …
We have explored a model for adsorption of water into slit-like nanochannels with two walls chemically modified by grafted polymer layers forming brushes. A version of density functional method is used as theoretical tools. The water-like fluid model adopted from the work of Clark et al. [Mol. Phys., 2006, 104, 3561] adequately reproduces the bulk vapour-liquid coexistence envelope. The polymer layer consists of chain molecules in the framework of pearl-necklace model. Each chain molecule is chemically bonded to the pore walls by a single terminating segment. Our principal focus is in the stud…
A theory is presented of the longitudinal dispersion of DNA under equilibrium confined in a nanochannel. Orientational fluctuations of the DNA chain build up to give rise to substantial fluctuations of the coil in the longitudinal direction of the channel. The translational and orientational degrees of freedom of the polymer are described by the Green function satisfying the usual Fokker-Planck equation. It is argued that this is analogous to the transport equation occurring in the theory of convective diffusion of particles in pipe flow. Moreover, Taylor's method may be used to reduce the Fok…
We study the influence of chain stiffness on droplet flow in a nano-channel, coated with semiflexible hydrophobic polymers by means of non-equilibrium molecular-dynamics simulations. The studied system is then a moving droplet in the slit channel, coexisting with its vapor and subjected to periodic boundary conditions in the flow direction. The polymer chains, grafted by the terminal bead to the confining walls, are described by a coarse-grained model that accounts for chain connectivity, excluded volume interactions and local chain stiffness. The rheological, frictional and dynamical properti…
Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favourably with pruned-enriched Rosenbluth method (P…
We report on a computational study of the statics and dynamics of long flexible linear polymers that spontaneously knot and unknot. Specifically, the equilibrium self-entanglement properties, such as the knotting probability, knot length and position, are investigated with extensive Monte Carlo sampling of chains of up to 15,000 beads. Tens of such equilibrated chains of up to 4, 096 beads are next used as starting points for Langevin dynamics simulations. The complex interplay of chain dynamics and self-knotting is addressed by monitoring the time evolution of various metric and entanglement …
The effect of a finite torque on semiflexible polymers in a confined environment is investigated. It is shown how a new lengthscale appears in the strongly confined limit. The influence of a torque on the extension of biopolymers in nanochannels is also touched upon and it is argued that the presence of a torque has a strong influence on the dimensions of nanochannels needed to prevent hairpins.
We present a numerical study of the effect of knotting on the ejection of flexible and semiflexible polymers from a spherical, virus-like capsid. The polymer ejection rate is primarily controlled by the knot, which moves to the hole in the capsid and then acts as a ratchet. Polymers with more complex knots eject more slowly and, for large knots, the knot type, and not the flexibility of the polymer, determines the rate of ejection. We discuss the relation of our results to the ejection of DNA from viral capsids and conjecture that this process has the biological advantage of unknotting the DNA…
Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local" and, for several ring polymer models, we provide both theoretical and numerical evidence that, at equilibrium, the non-local configurations are more likely than the local ones. These characterisations are based on a standard approach for measuring the "size" of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength i…
Entanglement statistics of polymers in a lattice tube and unknotting of 4-plats
University of Melbourne（墨尔本大学）；Hiroshima University（广岛大学）；Capilano University（卡皮拉诺大学）；University of Saskatchewan（萨斯喀彻温大学）；Sask Polytech（萨斯卡通理工大学）；University of California Davis（加州大学戴维斯分校）；Ochanomizu University（御茶水女子大学）
We show that the injection of polymer chains into nanochannels becomes easier as the channel becomes narrower. This counter intuitive result arises because of a decrease in the diffusive time scale of the chains with increasing confinement. The results are obtained by extending the de Gennes blob model of confined polymers, and confirmed by hybrid molecular dynamics - lattice-Boltzmann simulations.
The effect of a high Reynold's number, pressure-driven flow of a compressible gas on the conformation of an oligomer tethered to the wall of a square-channel is studied under both ideal solvent and poor solvent conditions using a hybrid multiparticle collision dynamics and molecular dynamics algorithm. Unlike previous studies, the flow field contains an elongational component in addition to a shear component as well as fluid slip near the walls and results in a Schmidt number for the polymer beads that is less than unity. In both solvent regimes the oligomer is found to extend in the direction…
We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semi-flexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rul…
