Gaussian semiflexible rings under angular and dihedral restrictions

Relaxation dynamics of semiflexible treelike small-world polymer networks

We study the relaxation dynamics of the polymer networks that are constructed based on a degree distribution specific to small-world networks. The employed building algorithm generates polymers with a large variety of architectures, thus allowing for a detailed study of the structural transition from a pure linear chain to dendritic polymer networks. This is done by varying a single parameter p, which measures the randomness in the degree of the network's nodes. The dynamics is investigated in the framework of the generalized Gaussian structures model by monitoring the influence of the parameter p and of the stiffness parameter q on the behavior of the relaxation quantities: averaged monomer displacement, storage modulus, and loss modulus. The structure properties of the constructed polymers are described by the mean-square radius of gyration. In the absence of stiffness, in the intermediate frequencies domain of the dynamical quantities we encounter different behaviours, such as a dendritic behavior followed by a linear one for very small values of p or a single well-marked dendritic behavior for higher values of p. The stiffness parameter q influences drastically the relaxation dynamics of these polymer networks and in general no evident scaling regions were encountered. However, for some values of the parameter set (p,q), such as (0.8,0.4), an extremely short constant slope region, less than one order of magnitude, was found.

Dynamics of Dual Scale-Free Polymer Networks

We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding a link between non-neighboring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameters' set ( γ , p ) , we encounter for these dynamical properties regions of constant in-between slope.

Force distribution in a semiflexible loop

Loops undergoing thermal fluctuations are prevalent in nature. Ringlike or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in terms of free energy, an average quantity, but it may also be impacted by local fluctuating forces acting within these systems. The full distribution of these forces can thus give us insights into mechanochemistry beyond the predictive capability of thermodynamics. In this paper, we study the force exerted by an inextensible semiflexible polymer constrained in a looped state. By using a simulation method termed "phase-space sampling," we generate the equilibrium distribution of chain conformations in both position and momentum space. We compute the constraint forces between the two ends of the loop in this chain ensemble using Lagrangian mechanics, and show that the mean of these forces is equal to the thermodynamic force. By analyzing kinetic and potential contributions to the forces, we find that the mean force acts in the direction of increasing extension not because of bending stress, but in spite of it. Furthermore, we obtain a distribution of constraint forces as a function of chain length, extension, and stiffness. Notably, increasing contour length decreases the average force, but the additional freedom allows fluctuations in the constraint force to increase. The force distribution is asymmetric and falls off less sharply than a Gaussian distribution. Our work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system.

Dynamics of flexible active Brownian dumbbells in the absence and the presence of shear flow

The dynamical properties of a flexible dumbbell composed of active Brownian particles are analytically analyzed. The dumbbell is considered as a simplified description of a linear active polymer. The two beads are independently propelled in directions which change in a diffusive manner. The relaxation behavior of the internal degree of freedom is tightly coupled to the dumbbell activity. The latter dominates the dynamics for strong propulsion. As is shown, limitations in bond stretching strongly influence the relaxation behavior. Similarly, under shear flow, activity determines the relaxation and tumbling behavior at strong propulsion. Moreover, shear leads to a preferred alignment and consequently to shear thinning. Thereby, a different power-law dependence on the shear rate compared to passive dumbbells under flow is found.

Marked difference in conformational fluctuation between giant DNA molecules in circular and linear forms

We performed monomolecular observations on linear and circular giant DNAs (208 kbp) in an aqueous solution by the use of fluorescence microscopy. The results showed that the degree of conformational fluctuation in circular DNA was ca. 40% less than that in linear DNA, although the long-axis length of circular DNA was only 10% smaller than that of linear DNA. Additionally, the relaxation time of a circular chain was shorter than that of a linear chain by at least one order of magnitude. The essential features of this marked difference between linear and circular DNAs were reproduced by numerical simulations on a ribbon-like macromolecule as a coarse-grained model of a long semiflexible, double-helical DNA molecule. In addition, we calculated the radius of gyration of an interacting chain in a circular form on the basis of the mean field model, which provides a better understanding of the present experimental trend than a traditional theoretical equation.

Dynamics of semiflexible recursive small-world polymer networks

One of the fundamental issues in polymer physics is to reveal the relation between the structures of macromolecules and their various properties. In this report, we study the dynamical properties of a family of deterministically growing semiflexible treelike polymer networks, which are built in an iterative method. From the analysis of the corresponding dynamical matrix we derive the solution for its eigenvalues and their multiplicities, making use of a combined numerical and analytical approach. The eigenvalue spectra allow us to investigate the mechanical relaxation forms in depth for different values of the stiffness parameter. We observe that the dynamics of semiflexible networks is sensitive to the stiffness parameter. Our work paves a way to explore the structures of the highly symmetric polymers and provides a comprehensive understanding of the role of semiflexibility for the regular treelike networks which possess a small-world feature.