Diffusion/Reaction in Confined Polymer Chains

A comparative study of the target search of end monomers of real and Rouse chains under spherical confinement

We study the dynamics of the end monomers of a real chain confined in a spherical cavity to search for a small target on the cavity surface using Langevin dynamics simulation. The results are compared and contrasted with those of a Rouse chain to understand the influence of excluded volume interactions on the search dynamics, as characterized by the first passage time (FPT). We analyze how the mean FPT depends on the cavity size Rb, the target size a, and the degree of confinement quantified by Rg/Rb, with Rg being the polymer radius of gyration in free space. As a basic finding, the equilibrium distribution of the end monomers of a real chain in a closed spherical cavity differs from that of a Rouse chain at a given Rg/Rb, which leads to the differences between the mean FPTs of real and Rouse chains. Fitting the survival probability S(t) by a multi-exponential form, we show that the S(t) of real chains exhibits multiple characteristic times at large Rg/Rb. Our simulation results indicate that the search dynamics of a real chain exhibit three characteristic regimes as a function of Rg/Rb, including the transition from the Markovian to non-Markovian process at Rg/Rb ≈ 0.39, along with two distinct regimes at 0.39 < Rg/Rb < 1.0 and Rg/Rb > 1.0, respectively, where S(t) exhibits a single characteristic time and multiple characteristic times.

Proper adsorptive confinement for efficient production of cyclic polymers: a dissipative particle dynamics study

Efficient production of cyclic polymers has been a hot topic in the past few decades. In this work, we found that an adsorptive porous template with an appropriate size has the capability to accelerate the ring closure of a linear polymer chain in a dilute solution with a higher yield. The restricted pore provides a confined space and the effect of its characteristics, such as pore size, shape and adsorption strength on cyclization time, is systematically studied by using dissipative particle dynamics simulations. As a prerequisite of cyclization in confinement, the entry process of linear precursors has been studied as well. Total production time is governed by a tradeoff between the size effect caused by decreasing the size of the pore and the adsorption of the pore. The strong size effect suppresses polymer entry but accelerates cyclization. The stronger adsorption promotes polymer entry but decelerates cyclization. According to our defined total production time, a small spherical confinement with strong adsorption results in a shorter total production time of cyclic polymers compared to that in free solution. If chain cyclization is permitted during its entering the confinement, the interplay between steric hindrance caused by pore size and adsorption provides an additional 'virtual' confinement at the boundary between confinement and free solution. In this case, an optimal cyclization time is observed with an appropriate adsorption strength under small confinement. Our results provide useful guidance for designing suitable porous templates for producing cyclic polymers with high efficiency.

Polymer Looping Is Controlled by Macromolecular Crowding, Spatial Confinement, and Chain Stiffness

We study by extensive computer simulations the looping characteristics of linear polymers with varying persistence length inside a spherical cavity in the presence of macromolecular crowding. For stiff chains, the looping probability and looping time reveal wildly oscillating patterns as functions of the chain length. The effects of crowding differ dramatically for flexible versus stiff polymers. While for flexible chains the looping kinetics is slowed down by the crowders, for stiffer chains the kinetics turns out to be either decreased or facilitated, depending on the polymer length. For severe confinement, the looping kinetics may become strongly facilitated by crowding. Our findings are of broad impact for DNA looping in the crowded and compartmentalized interior of living biological cells.

Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size

The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.

Lattice model of diffusion-limited bimolecular chemical reactions in confined environments

We study the effect of confinement on diffusion-limited bimolecular reactions within a lattice model where a small number of reactants diffuse among a much larger number of inert particles. When the number of inert particles is held constant, the rate of the reaction is slow for small reaction volumes due to limited mobility from crowding and for large reaction volumes due to the reduced concentration of the reactants. The reaction rate proceeds fastest at an intermediate confinement corresponding to a volume fraction near 50%. We generalize the model to off-lattice systems with hydrodynamic coupling and predict that the optimal reaction rate for monodisperse colloidal systems occurs when the volume fraction is approximately 19%. Finally, we discuss the implications of our model for bimolecular reactions inside cells and the dynamics of confined polymers.

Dynamics of a self-avoiding polymer chain in slit, tube, and cube confinements

Monte Carlo simulations are presented for the observation of the dynamics of a self-avoiding polymer in three types of confinement: slit, tube, and cube. We pay special attention to the parameter regime where the characteristic confinement dimension is smaller than the radius of gyration of the unconfined polymer. On the basis of the bond-fluctuation model, we measured the rotation time of the end-to-end vector of the polymer, the diffusion time for the center of the polymer to move a distance comparable to the root mean square end-to-end distance, and the looping time for the ends of the polymer to approach each other from an open position. As functions of the confinement width and polymer length, these three time scales are discussed in light of scaling theories.