Translocation of a flexible polymer through a cone-shaped channel is studied, theoretically and using computer simulations. Our simulations show that the shape of the channel causes the polymer translocation to be a driven process. The effective driving force of entropic origin acting on the polymer is calculated as a function of the length and the apex-angle of the channel, theoretically. It is found that the translocation time is a non-monotonic function of the apex-angle of the channel. By increasing the apex-angle from zero, the translocation time shows a minimum and then a maximum. Also, it is found that regardless of the value of the apex-angle, the translocation time is a uniformly decreasing function of the channel length. The results of the theory and the simulation are in good qualitative agreement.
The nano-scale confinement of polymers in cone-shaped geometries occurs in many experimental situations. A flexible polymer confined in a cone-shaped nano-channel is studied theoretically and by using molecular dynamics simulations. Distribution of the monomers inside the channel, configuration of the confined polymer, the entropic force acting on the polymer, and their dependence on the channel and the polymer parameters are investigated. The theory and the simulation results are in very good agreement. The entropic force on the polymer that results from the asymmetric shape of the channel is measured in the simulations and its magnitude is found to be significant relative to thermal energy. The obtained dependence of the force on the channel parameters may be useful in the design of cone-shaped nano-channels.
Here we report on the translocation of folded polymers through nano-pores using molecular dynamic simulations. Two cases are studied: one in which a folded molecule unfolds upon passage and one in which the folding remains intact as the molecule passes through the nano-pore. The topology of a folded polymer chain is defined as the arrangement of the intramolecular contacts, known as circuit topology. In the case where intramolecular contacts remain intact, we show that the dynamics of passage through a nano-pore varies for molecules with differing topologies: a phenomenon that can be exploited to enrich certain topologies in mixtures. We find that the nano-pore allows reading of the topology for short chains. Moreover, when the passage is coupled with unfolding, the nano-pore enables discrimination between pure states, i.e., states in which the majority of contacts are arranged identically. In this case, as we show here, it is also possible to read the positions of the contact sites along a chain. Our results demonstrate the applicability of nano-pore technology to characterize and sort molecules based on their topology.
The distribution of counterions and the electrostatic interaction between two similarly charged dielectric slabs is studied in the strong coupling limit. Dielectric inhomogeneities and discreteness of charge on the slabs have been taken into account. It is found that the amount of dielectric constant difference between the slabs and the environment, and the discreteness of charge on the slabs have opposing effects on the equilibrium distribution of the counterions. At small inter-slab separations, increasing the amount of dielectric constant difference increases the tendency of the counterions toward the middle of the intersurface space between the slabs and the discreteness of charge pushes them to the surfaces of the slabs. In the limit of point charges, independent of the strength of dielectric inhomogeneity, counterions distribute near the surfaces of the slabs. The interaction between the slabs is attractive at low temperatures and its strength increases with the dielectric constant difference. At room temperature, the slabs may completely attract each other, reach to an equilibrium separation or have two equilibrium separations with a barrier in between, depending on the system parameters.
The electric-field-driven entry process of flexible charged polymers such as single-stranded DNA (ssDNA) into asymmetric nanoscale channels such as the α-hemolysin protein channel is studied theoretically and using molecular dynamics simulations. Dependence of the height of the free-energy barrier on the polymer length, the strength of the applied electric field, and the channel entrance geometry is investigated. It is shown that the squeezing effect of the driving field on the polymer and the lateral confinement of the polymer before its entry to the channel crucially affect the barrier height and its dependence on the system parameters. The attempt frequency of the polymer for passing the channel is also discussed. Our theoretical and simulation results support each other and describe related data sets of polymer translocation experiments through the α-hemolysin protein channel reasonably well.
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