Related papers: Proteins analysed as virtual knots
The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of…
Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in…
Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…
The understanding of dynamics and functioning of biological membranes and in particular of membrane embedded proteins is one of the most fundamental problems and challenges in modern biology and biophysics. In particular the impact of…
For their resilience and toughness, filamentous entanglements are ubiquitous in both natural and engineered systems across length scales, from polymer-chain- to collagen-networks and from cable-net structures to forest canopies. Textiles…
Folded linear molecular chains are ubiquitous in biology. Folding is mediated by intra-chain interactions that "glue" two or more regions of a chain. The resulting fold topology is widely believed to be a determinant of biomolecular…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
We define new notions of groups of virtual and welded knots (or links) and we study their relations with other invariants, in particular the Kauffman group of a virtual knot.
Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff…
Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups…
In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological invariants over the filtration of point cloud data using…
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…
This paper extends the construction of invariants for virtual knots to virtual long knots and introduces two new invariant modules of virtual long knots. Several interesting features are described that distinguish virtual long knots from…
This thesis details a Python-based software designed to calculate the Jones polynomial, a vital mathematical tool from Knot Theory used for characterizing the topological and geometrical complexity of curves in \( \mathbb{R}^3 \), which is…
Identification and alignment of three-dimensional folding of proteins may yield useful information about relationships too remote to be detected by conventional methods, such as sequence comparison, and may potentially lead to prediction of…
Exploring the structural topology of genome-based large-scale metabolic network is essential for investigating possible relations between structure and functionality. Visualization would be helpful for obtaining immediate information about…
Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products and they can act as substrates for further rounds of…
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…
The transport of DNA polymers through nanoscale pores is central to many biological processes, from bacterial gene exchange to viral infection. In single-molecule nanopore sensing, the detection of nucleic acid and protein analytes relies…