Related papers: How molecular knots can pass through each other
Motivated by recent advances in single molecule manipulation techniques that enabled several groups to tie knots in individual polymer strands and to monitor their dynamics, we have used computer simulations to study "friction knots"…
Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model…
We discuss multiscale simulations of long biopolymer translocation through wide nanopores that can accommodate multiple polymer strands. The simulations provide clear evidence of folding quantization, namely, the translocation proceeds…
We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across…
Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on…
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…
An extensive study of single block copolymer knots containing two kinds of monomers $A$ and $B$ is presented. The knots are in a solution and their monomers are subjected to short range interactions that can be attractive or repulsive. In…
We construct a new statistical physical model of polymer translocation through a pore in a membrane treated as the diffusion process across a free energy barrier. We determine the translocation time in terms of chain flexibility yielding an…
Knots are fascinating topological structures that have been observed in various contexts, ranging from micro-worlds to macro-systems, and are conjectured to play a fundamental role in their respective fields. In order to characterize their…
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…
We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting…
We consider the generalization of the Kramers escape over a barrier problem to the case of a long chain molecule. It involves the motion of chain molecule of N segments across a region where the free energy per segment is higher, so that it…
We illustrate schematically a possible traversing along the path of trefoil-type and $8_{18}$ knots during a specific time period by considering a quantum-mechanic system which satisfies a specific kind of phase dynamics of quantum…
We consider the generalization of the Kramers escape over a barrier problem to the case of a long chain molecule. The problem involves the motion of a chain molecule of $N$ segments across a region where the free energy per segment is…
We study knotted polymers in equilibrium with an array of obstacles which models confinement in a gel or immersion in a melt. We find a crossover in both the geometrical and the topological behavior of the polymer. When the polymers' radius…
Macromolecules can gain special properties by adopting knotted conformations, but engineering knotted macromolecules is a challenging task. Here we surprisingly observed that knotting can be very effectively produced in active polymers.…
This report presents a unified treatment of the density of states for the knots and folds of polymer chains. The physical realization of such systems ranges from DNA molecules to the microscopic configurations of space-time.
Semiflexible polymers are widely used as a paradigm for understanding structural phases in biomolecules including folding of proteins. Here, we compare bead-spring and bead-stick variants of coarse-grained semiflexible polymer models that…
A barrier penetration model has been proposed to explain the spontaneous melting of the DNA oligomers into two separate single strands whereas the partially melted intermediate states are shown to be the bound state solution of the same…
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…