Related papers: Matrix representation of knots and folds: I
This paper visualizes a knot reduction algorithm
A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The…
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we…
The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological…
The density of states contains all informations on energetic quantities of a statistical system, such as the mean energy, free energy, entropy, and specific heat. As a specific application, we consider in this work a simple lattice model…
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly…
The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction…
The densities of states are evaluated for very short chain molecules made up of overlapping monomers, using a model which has previously been shown to produce helical structure. The results of numerical calculations are presented for…
This is an expository article on diagrammatic representations of knots and links in various settings via braids.
We make use of the previously developed formalism for a monomer ensemble and include angular dependence of the segments of the polymer chains thus described. In particular we show how to deal with stiffness when the polymer chain is…
We study the dynamics of a single chain polymer confined to a two dimensional cell. We introduce a kinetically constrained lattice gas model that preserves the connectivity of the chain, and we use this kinetically constrained model to…
We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N=55 using exact enumeration…
The most tight conformations of prime knots are found with the use of the SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry of the knots is analysed. Connections with the physics of polymers are discussed.
We demonstrate how an effective density of states can be derived from the S-matrix describing a coupled-channel system. Besides the locations of poles, the phase of the determinant of the S-matrix encodes essential details in characterizing…
Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses -- one yielding an energy penalty for…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide…
We propose a mechanism in which two molecular knots pass through each other and swap positions along a polymer strand. Associated free energy barriers in our simulations only amount to a few $k_{B}T$, which may enable the interchange of…
We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through…
We present results relevant to the equilibrium organization of DNA strands of arbitrary length interacting with a spherical organizing center, suggestive of DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in which a…
Synthetic polymers are versatile and widely used materials. Similar to small organic molecules, a large chemical space of such materials is hypothetically accessible. Computational property prediction and virtual screening can accelerate…