Segregation of ring polyelectrolytes in nano-channel

Equilibrium behaviour of two cavity-confined polymers: effects of polymer width and system asymmetries

Experiments using nanofluidic devices have proven effective in characterizing the physical properties of polymers confined to small cavities. Two recent studies using such methods examined the organization and dynamics of two DNA molecules in box-like cavities with strong confinement in one direction and with square and elliptical cross sections in the lateral plane. Motivated by these experiments, we employ Monte Carlo and Brownian dynamics simulations to study the physical behaviour of two polymers confined to small cavities with shapes comparable to those used in the experiments. We quantify the effects of varying the following polymer properties and confinement dimensions on the organization and dynamics of the polymers: the polymer width, the polymer contour length ratio, the cavity cross-sectional area, and the degree of cavity elongation for cavities with rectangular and elliptical cross sections. We find that the tendency for polymers to segregate is enhanced by increasing polymer width. For sufficiently small cavities, increasing cavity elongation promotes segregation and localization of identical polymers to opposite sides of the cavity along its long axis. A free-energy barrier controls the rate of polymers swapping positions, and the observed dynamics are roughly in accord with predictions of a simple theoretical model. Increasing the contour length difference between polymers significantly affects their organization in the cavity. In the case of a large linear polymer co-trapped with a small ring polymer in an elliptical cavity, the small polymer tends to lie near the lateral confining walls, and especially at the cavity poles for highly elongated ellipses.

Equilibrium organization, conformation, and dynamics of two polymers under box-like confinement

Motivated by recent nanofluidics experiments, we use Brownian dynamics and Monte Carlo simulations to study the conformation, organization and dynamics of two polymer chains confined to a single box-like cavity. The polymers are modeled as flexible bead-spring chains, and the box has a square cross-section of side length L and a height that is small enough to compress the polymers in that dimension. For sufficiently large L, the system behaviour approaches that of an isolated polymer in a slit. However, the combined effects of crowding and confinement on the polymer organization, conformation and equilibrium dynamics become significant when where is the transverse radius of gyration for a slit geometry. In this regime, the centre-of-mass probability distribution in the transverse plane exhibits a depletion zone near the centre of the cavity (except at very small L) and a 4-fold symmetry with quasi-discrete positions. Reduction in polymer size with decreasing L arises principally from confinement rather than inter-polymer crowding. By contrast, polymer diffusion and internal motion are strongly affected by inter-polymer crowding. The two polymers tend to occupy opposite positions relative to the box centre, about which they diffuse relatively freely. Qualitatively, this static and dynamical behaviour differs significantly from that previously observed for confinement of two polymers to a narrow channel. The simulation results for a suitably chosen box width are qualitatively consistent with results from a recent experimental study of two λ-DNA chains confined to a nanofluidic cavity.

Free energy and segregation dynamics of two channel-confined polymers of different lengths

Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere polymers under confinement in a cylindrical channel. We focus on the effects of using polymers of different lengths. We measure the variation of the conformational free energy, F, with the center-of-mass separation distance, λ. The simulations reveal four different separation regimes, characterized by different scaling properties of the free energy with respect to the polymer lengths and the channel diameter, D. We propose a regime map in which the state of the system is determined by the values of the quantities N_{2}/N_{1} and λ/(N_{1}+N_{2})D^{-β}, where N_{1} and N_{2} are the polymer lengths, and where β≈0.64. The observed scaling behavior of F(λ) in each regime is in reasonable agreement with predictions using a simple theoretical model. In addition, we use MC dynamics simulations to study the segregation dynamics of initially overlapping polymers by measurement of the incremental mean first-passage time with respect to λ. For systems characterized by a wide range of λ in which a short polymer is nested within a longer one, the segregation dynamics are close to that expected for two noninteracting one-dimensional random walkers undergoing unbiased diffusion. When the free-energy gradient is large, segregation is rapid and characterized by out-of-equilibrium effects.