Related papers: Proteins analysed as virtual knots
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…
This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.
The ability to consistently distinguish real protein structures from computationally generated model decoys is not yet a solved problem. One route to distinguish real protein structures from decoys is to delineate the important physical…
Molecular dynamics simulations of folding in an off-lattice protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their…
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by…
We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate…
As proteins with similar structures often have similar functions, analysis of protein structures can help predict protein functions and is thus important. We consider the problem of protein structure classification, which computationally…
In this paper, we give a geometric interpretation of virtual knotoids as arcs in thickened surfaces. Then we show that virtual knotoid theory is a generalization of classical knotoid theory. This gives a proof of a conjecture of Kauffman…
Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent…
Prediction of protein-ligand complexes for flexible proteins remains still a challenging problem in computational structural biology and drug design. Here we present two novel deep neural network approaches with significant improvement in…
In this letter, the possible dynamic scaling properties of protein molecules in folding are investigated theoretically by assuming that the protein molecules are percolated networks. It is shown that the fractal character and the fractal…
DNA unzipping by nanopore translocation has implications in diverse contexts, from polymer physics to single-molecule manipulation to DNA-enzyme interactions in biological systems. Here we use molecular dynamics simulations and a…
It is shown that a small subset of modes which are likely to be involved in protein functional motions of large amplitude can be determined by retaining the most robust normal modes obtained using different protein models. This result…
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…
Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins. However, an algorithm that describes the…
Protein-ligand scoring is an important step in a structure-based drug design pipeline. Selecting a correct binding pose and predicting the binding affinity of a protein-ligand complex enables effective virtual screening. Machine learning…
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In…
It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-dimensional submanifold of a closed orientable 3-manifold can be realised…
In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques,…
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…