A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Mathematical pipeline identifies structural homology of knotted proteins.
New method detects and compares folding pathways of knotted proteins.
Persistent homology can recognize knotting in curves.
Model proteins with bonds using Kauffman bracket skein module.
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 disappear rapidly under manipulation and interaction. Knotting has been previou…
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 97% of proteins are, however, classified as unknots when intra-chain interaction…
Method optimizes knotting pathways in constrained polymers.
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 curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluatin…
Classifies uncolored bonded knots with up to 7 singularity points.
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, knotoids are diagrams representing projections of open curves in 3D space, in contras…
The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surgery. Band surgeries on a 2-bridge knot N((4mn-1)/(2m)) yielding a (2,2k)-torus link are characterized. We apply this and other rational tangl…
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 the relation between knotoids differing only by small perturbations of the direc…
Focusing on a small set of proteins that i) fold in a concerted, all-or-none fashion and ii) do not contain knots or slipknots, we show that the Gauss linking integral, the torsion and the number of sequence-distant contacts provide information regarding the folding rate. Our results suggest that the global topology/ge…
We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA segments. We analyze such experiments for the Mu protein-DNA complex. We characterize t…
New method analyzes knots and links using multiscale Gauss link integral.
Polynomial invariants classify molecular chains based on their contact arrangements.
Graphoids are topological invariants of virtual graph diagrams.
Uniform Closure Method and Bayes classifier perform similarly in classifying open knots.
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 provide a framework for working with subknots inside of knot diagrams via knotoid dia…
We equip a knot with a set of colored bonds, that is, colored intervals properly embedded into . Such a construction can be viewed as a structure that topologically models a closed protein chain including any type of bridges connecting the backbone residues. We introduce an invariant of su…
Complete classification of knotoids up to seven crossings.
The effective representation of proteins is a crucial task that directly affects the performance of many bioinformatics problems. Related proteins usually bind to similar ligands. Chemical characteristics of ligands are known to capture the functional and mechanistic properties of proteins suggesting that a ligand base…
This paper is a survey on the theory of knotoids and braidoids. Knotoids are open ended knot diagrams in surfaces and braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids in the plane. We survey through the fundamental notions and existing works on these …
A new framework uses text descriptions to improve protein design.
Developed algebraic theory of bonded braids, proving Markov theorem.
Knots have been considered to be useful models for simulating molecular chains such as DNA and proteins. One quantity that we are interested on molecular knots is the minimum number of monomers necessary to realize a knot. In this paper we consider every knot in the cubic lattice. Especially the minimal length of a kno…
Deep learning models optimize protein sequences.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
Machine learning reveals hidden features in knot classification.
Integrase proteins acting on circular double-stranded DNA often change its topology by transforming unknotted circles into torus knots and links. Two systems of tangle equations--corresponding to the two initial DNA sequences--arise when modelling this transformation: direct and inverted. With no a priori assumptions o…
ProGen models protein sequences for synthetic biology.
Solvents can induce helical knots in simulated biopolymer tubes.
New 3D protein analysis methods improve accuracy.
Proteins are commonly used by biochemical industry for numerous processes. Refining these proteins' properties via mutations causes stability effects as well. Accurate computational method to predict how mutations affect protein stability are necessary to facilitate efficient protein design. However, accuracy of predic…
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of a knot i…
PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.
A new model explains protein interactions via electron delocalization.
EBM predicts protein conformations at atomic scale using crystallized data.
Experimental determination of protein function is resource-consuming. As an alternative, computational prediction of protein function has received attention. In this context, protein structural classification (PSC) can help, by allowing for determining structural classes of currently unclassified proteins based on thei…
Protein interactions constitute the fundamental building block of almost every life activity. Identifying protein communities from Protein-Protein Interaction (PPI) networks is essential to understand the principles of cellular organization and explore the causes of various diseases. It is critical to integrate multipl…
Mathematician summarizes protein geometry and mutation effects.
EGR refines and assesses protein complex structures.
We introduce a new model of proteins, which extends and enhances the traditional graphical representation by associating a combinatorial object called a fatgraph to any protein based upon its intrinsic geometry. Fatgraphs can easily be stored and manipulated as triples of permutations, and these methods are therefore a…
Two proteins are homologous if they have a common evolutionary origin, and the binary classification problem is to identify proteins in a candidate set that are homologous to a particular native protein. The feature (explanatory) variables available for classification are various measures of similarity of proteins. The…
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 classifies the structures of proteins into pre-defined groups. We develop a weight…
Flexible Kernels for Protein Property Prediction
New method steers protein design towards desired properties.
A new diffusion model generates novel protein backbones without relying on pretrained networks.