Related papers: Sequence determines degree of knottedness in a coa…
Proteins can sometimes be knotted, and for many reasons the study of knotted proteins is rapidly becoming very important. For example, it has been proposed that a knot increases the stability of a protein. Knots may also alter enzymatic…
We perform theoretical studies of stretching of 20 proteins with knots within a coarse grained model. The knot's ends are found to jump to well defined sequential locations that are associated with sharp turns whereas in homopolymers they…
Knotted proteins embed a physical (i.e., open) knot within their native structures. For decades, significant effort has been devoted to elucidating the functional role of knots in proteins, yet no consensus has been reached. Here, using…
Semiflexible polymer models are widely used as a paradigm to understand structural phases in biomolecules including folding of proteins. Since stable knots are not so common in real proteins, the existence of stable knots in semiflexible…
A number of recently discovered protein structures incorporate a rather unexpected structural feature: a knot in the polypeptide backbone. These knots are extremely rare, but their occurrence is likely connected to protein function in as…
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…
We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
Although rare, an increasing number of proteins have been observed to contain entanglements in their native structures. To gain more insight into the significance of protein knotting, researchers have been investigating protein knot…
Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase…
We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers.…
Spontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting and knot complexity increase by orders of magnitude in diblock polymers with a fraction…
A small fraction of all protein structures characterized so far are entangled. The challenge of understanding the properties of these knotted proteins, and the why and the how of their natural folding process, has been taken up in the past…
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…
Background: Designing amino acid sequences that are stable in a given target structure amounts to maximizing a conditional probability. A straightforward approach to accomplish this is a nested Monte Carlo where the conformation space is…
Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…
Native protein folds often have a high degree of symmetry. We study the relationship between the symmetries of native proteins, and their designabilities -- how many different sequences encode a given native structure. Using a…
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also abound in viral DNA packaged inside bacteriophages. RNA molecules, on 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…
We study the statistical properties of hydrophobic/polar model sequences with unique native states on the square lattice. It is shown that this ensemble of sequences differs from random sequences in significant ways in terms of both the…