Related papers: Proteins analysed as virtual knots
The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the…
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types,…
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…
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…
Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here we investigate…
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…
We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely,…
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…
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…
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…
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…
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…
Knotted molecules occur naturally and are designed by scientists to gain special biological and material properties. Understanding and utilizing knotting require efficient methods to recognize and generate knotted structures, which are…
Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence…
The entanglement of open curves in 3-space appears in many physical systems and affects their material properties and function. A new framework in knot theory was introduced recently, that enables to characterize the complexity of…
Understanding the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geometry of knotted proteins by analysing the distribution of a…
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…
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…
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular…
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systematically analyzes protein structures. We showcase this…