Packaging-ejection phase transitions of a polymer chain: Theory and Monte Carlo simulation

Polymer translocation into cavities: Effects of confinement geometry, crowding, and bending rigidity on the free energy

Monte Carlo simulations are used to study the translocation of a polymer into a cavity. Modeling the polymer as a hard-sphere chain with a length up to N=601 monomers, we use a multiple-histogram method to measure the variation of the conformational free energy of the polymer with respect to the number of translocated monomers. The resulting free-energy functions are then used to obtain the confinement free energy for the translocated portion of the polymer. We characterize the confinement free energy for a flexible polymer in cavities with constant cross-sectional area A for various cavity shapes (cylindrical, rectangular, and triangular) as well as for tapered cavities with pyramidal and conical shape. The scaling of the free energy with cavity volume and translocated polymer subchain length is generally consistent with predictions from simple scaling arguments, with small deviations in the scaling exponents likely due to finite-size effects. The confinement free energy depends strongly on cavity shape anisometry and is a minimum for an isometric cavity shape with a length-to-width ratio of unity. Entropic depletion at the edges or vertices of the confining cavity are evident in the results for constant-A and pyramidal cavities. For translocation into infinitely long cones, the scaling of the free energy with taper angle is consistent with a theoretical prediction employing the blob model. We also examine the effects of polymer bending rigidity on the translocation free energy for cylindrical cavities. For isometric cavities, the observed scaling behavior is in partial agreement with theoretical predictions, with discrepancies arising from finite-size effects that prevent the emergence of well-defined scaling regimes. In addition, translocation into highly anisometric cylindrical cavities leads to a multistage folding process for stiff polymers. Finally, we examine the effects of crowding agents inside the cavity. We find that the confinement free energy increases with crowder density. At constant packing fraction the magnitude of this effect lessens with increasing crowder size for a crowder-to-monomer size ratio ≥1.

DNA packaging in viral capsids with peptide arms

Strong chain rigidity and electrostatic self-repulsion of packed double-stranded DNA in viruses require a molecular motor to pull the DNA into the capsid. However, what is the role of electrostatic interactions between different charged components in the packaging process? Though various theories and computer simulation models were developed for the understanding of viral assembly and packaging dynamics of the genome, long-range electrostatic interactions and capsid structure have typically been neglected or oversimplified. By means of molecular dynamics simulations, we explore the effects of electrostatic interactions on the packaging dynamics of DNA based on a coarse-grained DNA and capsid model by explicitly including peptide arms (PAs), linked to the inner surface of the capsid, and counterions. Our results indicate that the electrostatic interactions between PAs, DNA, and counterions have a significant influence on the packaging dynamics. We also find that the packed DNA conformations are largely affected by the structure of the PA layer, but the packaging rate is insensitive to the layer structure.

The Semiflexible Polymer Translocation into Laterally Unbounded Region between Two Parallel Flat Membranes

Using the dynamic Monte Carlo method, we investigate dynamics of semiflexible polymer translocation through a nanopore into laterally unbounded region between two parallel flat membranes with separation R in presence of an electric field inside the pore. The average translocation time τ initially decreases rapidly with increase of R in the range of R < 10 and then almost keeps constant for R ≥ 10, and the decline range increases with increase of dimensionless bending stiffness κ. We mainly study the effect of chain length N, κ and electric field strength E on the translocation process for R = 5. The translocation dynamics is significantly altered in comparison to an unconfined environment. We find τ ~ N^α, where the exponent α increases with increase of E for small κ. α initially increases slowly with increase of E and then keeps constant for moderate κ. α decreases with increase of E for large κ. However, α decreases with increase of κ under various E. In addition, we find τ ~ κ^β. β decreases with increase of N under various E. These behaviors are interpreted in terms of the probability distribution of translocation time and the waiting time of an individual monomer segment passing through the pore during translocation.

Dynamics and limitations of spontaneous polyelectrolyte intrusion into a charged nanocavity

We systematically investigate the spontaneous packaging mechanism of a single polyelectrolyte chain into an oppositely charged nanocavity by Langevin molecular dynamics simulations of a generic coarse-grained model. Intrusion dynamics and packaging rate, as well as the self-assembly process inside turn out to depend sensitively on the stiffness of the polyelectrolyte, the surface charge density inside the capsid, and the radius of the cavity. Further analysis shows that, depending on the stiffness, thermal fluctuations and charge inversion can be important factors to overcome barriers that slow down the intrusion and packaging dynamics. These results help advance our understanding of the function of charges on the inner surface of viral capsids and the possibility to design capsids as synthetic nanocarriers.

Domain patterns in a diblock copolymer-diblock copolymer mixture with oscillatory particles

We investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-diblock copolymer mixtures in the presence of periodic oscillatory particles. Under certain conditions, although the macrophase separation of a system is almost isotropic, microphase separation of one diblock copolymer takes place and becomes anisotropic gradually. By changing the oscillatory frequency and amplitude, the orientational order transition of a striped microphase structure from the state parallel to the oscillatory direction to the state perpendicular to the oscillatory direction is observed. We also find that the order transition occurs when we change the initial composition ratio. Furthermore, we examine the domain size and the orientational order parameter of microstructure in the process of orientational order transition. The results may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition of soft materials by changing the oscillatory field.