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The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (kloop) of the loop formation would be inversely proportional to viscosity (η), i.e., kloop ∼ η−1. Experiments and simulations showed, however, that kloop showed the fractional viscosity dependence of kloop ∼ η−β with β < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully. [ABSTRACT FROM AUTHOR]

The ejection of a single polymer chain out of confinement is a ubiquitous phenomenon in various engineering and biological processes. A virus, for example, ejects a DNA from its viral capsid to a host cell in order to infect the host. The ejection of a polymer chain is often relatively fast such that the polymer hardly relaxes its conformation and stays in nonequilibrium states during the ejection. However, the effects of the nonequilibrium conformation on the ejection process still remain unanswered, especially when a complicated conformation such as a knot exists. In this study, we employ a generic coarse-grained model and perform extensive molecular simulations to investigate how the knot and its conformational relaxation would affect the kinetics of the ejection process. We find that the ejection becomes slower by a factor of nine or more when the polymer chain forms a knot conformation inside the confinement. The knot conformation makes the polymer chain highly tensed, thus hindering the polymer from being pulled from the capsid. In order to investigate the effect of the knot and its conformational relaxation systematically, we tune the molecular parameters of the polymer chain and control the degree of relaxation of the knot conformation. The relaxation of the knot conformation facilitates the ejection process significantly. [ABSTRACT FROM AUTHOR]

The conformational relaxation of a polymer chain often slows down in various biological and engineering processes. The polymer, then, may stay in nonequilibrium states throughout the process such that one may not invoke the local thermal equilibrium (LTE) approximation, which has been usually employed to describe the kinetics of various processes. In this work, motivated by recent single-molecule experiments on DNA packaging into a viral capsid, we investigate how the nonequilibrium conformations and the LTE approximation would affect the packaging of a polymer chain into small confinement. We employ a simple but generic coarse-grained model and Langevin dynamics simulations to investigate the packaging kinetics. The polymer segments (both inside and outside the confinement) stay away from equilibrium under strong external force. We devise a simulation scheme to invoke the LTE approximation during packaging and find that the relaxation of nonequilibrium conformations plays a critical role in regulating the packaging rate. [ABSTRACT FROM AUTHOR]

The conformation and its relaxation of a single polymer depend on solvent quality in a polymer solution: a polymer collapses into a globule in a poor solvent, while the polymer swells in a good solvent. When one translocates a polymer through a narrow pore, a drastic conformational change occurs such that the kinetics of the translocation is expected to depend on the solvent quality. However, the effects of solvent quality on the translocation kinetics have been controversial. In this study, we employ a coarse-grained model for a polymer and perform Langevin dynamics simulations for the driven translocation of a polymer in various types of solvents. We estimate the free energy of polymer translocation using steered molecular dynamics simulations and Jarzynski's equality and find that the free energy barrier for the translocation increases as the solvent quality becomes poorer. The conformational entropy contributes most to the free energy barrier of the translocation in a good solvent, while a balance between entropy and energy matters in a poor solvent. Interestingly, contrary to what is expected from the free energy profile, the translocation kinetics is a non-monotonic function of the solvent quality. We find that for any type of solvent, the polymer conformation stays far away from the equilibrium conformation during translocation due to an external force and tension propagation. However, the degree of tension propagation differs depending on the solvent quality as well as the magnitude of the external force: the tension propagation is more significant in a good solvent than in a poor solvent. We illustrate that such differences in tension propagation and non-equilibrium conformations between good and poor solvents are responsible for the complicated non-monotonic effects of solvent quality on the translocation kinetics. [ABSTRACT FROM AUTHOR]