22 papers · ranked by Valyu relevance
Álvaro Torras-Casas, Ka Man Yim, Ulrich Pennig
Given a poset-graded chain complex of vector spaces, a Conley complex is the minimal chain-homotopic reduction of the initial complex that respects the poset grading. A connection matrix is a matrix representing the differential of the Conley complex. In this work, we give an algebraic derivation of the Conley complex…
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We use coarse-grained simulations to study the impact of charge regulation on the complexation of a weak polyacid and a strong polycation. Comparing an isolated polyacid with the polyelectrolyte pair, we demonstrate that charge regulation leads to a significant enhancement of the ionization. Furthermore, our…
Tunde Aderinwale, Rashidedin Jahandideh, Zicong Zhang, Bowen Zhao + 2 more
Various biological processes in living cells are carried out by protein complexes, whose interactions can span across multiple protein structures. To understand the molecular mechanisms of such processes, it is crucial to know the quaternary structures of these complexes. Although the structures of many protein…
Yingnan Hou, Tengyu Xie, Liuqing He, Liang Tao + 1 more
AlphaFold is making great progress in protein structure prediction, not only for single-chain proteins but also for multi-chain protein complexes. When using AlphaFold-Multimer to predict protein–protein complexes, we observed some unusual structures in which chains are looped around each other to form topologically…
Patrick Bryant, Gabriele Pozzati, Wensi Zhu, Aditi Shenoy + 2 more
AlphaFold and AlphaFold-multimer can predict the structure of single- and multiple chain proteins with very high accuracy. However, predicting protein complexes with more than a handful of chains is still unfeasible, as the accuracy rapidly decreases with the number of chains and the protein size is limited by the…
Anatoly Golovnev, Alireza Mashaghi
Title: Summary A wide range of physical systems can be formally mapped to a linear chain of sorted objects. Upon introduction of intrachain interactions, such a chain can “fold” to elaborate topological structures, analogous to folded linear polymer systems. Two distinct chain-topology theories, knot theory and circuit…
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The structural complexities of polymer networks, i.e., multiple functional groups, diverse connection sites, and various defects, make it difficult to accurately describe their microstructure using theoretical models and traditional metrics such as cross-link density (XLD). This study uses multi-scale molecular…
Toby G. Johnson, A. James Link
Tail of Mechanically Interlocked Peptides Authors: Toby G. Johnson, A. James Link First synthesized by chemists in the 1960s, mechanically interlocked molecules (MIMs) were created out of scientific curiosity and thought only to be academic oddities. However, naturally occurring interlocked biomolecules were…
Luca Tubiana, Angelo Rosa, F. Fragiacomo, Cristian Micheletti
We report on a computational study of the statics and dynamics of long flexible linear polymers that spontaneously knot and unknot. Specifically, the equilibrium self-entanglement properties, such as the knotting probability, knot length and position, are investigated with extensive Monte Carlo sampling of chains of up…
Jonathan J. Danon, David A. Leigh, Simone Pisano, Alberto Valero + 1 more
'Iñigo J. Vitorica‐Yrezabal'] Title: Abstract A molecular link (a six crossing, doubly interlocked, [2]catenane with twisted rings) and a 31#31 granny knot (a composite knot made up of two trefoil tangles of the same handedness) were constructed by ring-closing olefin metathesis of an iron(II)-coordinated 2×2…
Guzmán Gil-Ramírez, David A Leigh, Alexander J Stephens
Half a century after Schill and Lüttringhaus carried out the first directed synthesis of a [2]catenane, a plethora of strategies now exist for the construction of molecular Hopf links (singly interlocked rings), the simplest type of catenane. The precision and effectiveness with which suitable templates and/or…
Jonas Berx, Alireza Mashaghi
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single isolated folded linear chains, the number and arrangement of contacts within the…
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RNA molecules fold into complex three-dimensional structures that determine their function. A wide range of mathematical frameworks, such as chord diagrams, fatgraphs, and context-free grammars, have been used to represent these structures; however, these models have largely been developed from mathematical motivations…
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Sequence is the critical determinant of macromolecular function, yet current polymer design approaches often optimize monomer composition and ratios while ignoring sequence. This creates poorly defined design spaces for active learning that miss the vast combinatorial landscape of sequence possibilities. We introduce…
Jonas Berx, Alireza Mashaghi
Circuit topology employs fundamental units of entanglement, known as soft contacts, for constructing knots from the bottom up, utilizing circuit topology relations, namely parallel, series, cross, and concerted relations. In this article, we further develop this approach to facilitate the analysis of chirality, which…
S. K. Nechaev
| I. Introduction: | What we are talking about? | 2 | | --- | --- | --- | | II. Milestones | | 5 | | A. Abelian epoch | | 5 | | B. Non-Abelian epoch | | 6 | | | 1. Methods of algebraic topology in polymer statistics. Topology as quenched | | | disorder | | 7 | | | 2. How to define the knot complexity? | 7 | | | 3.…
Da Xu, Lee-Shin Chu, Jeffrey J. Gray
Co-folding models like AlphaFold have revolutionized protein complex structure prediction, yet their reliance on multiple sequence alignments (MSAs) limits their applicability on challenging targets such as antibody-antigen complexes. An alternative approach, structure-based protein-protein docking, predicts the…
Dongfang Zhao
The state-of-the-art techniques for processing crossblockchain transactions take a simple centralized approach: when the assets on blockchain X, say X-coins, are exchanged with the assets on blockchain Y —the Y -coins, those X-coins need to be exchanged to a "middle" medium (such as Bitcoin) that is then exchanged to Y…
Jonathon E Beves, Jonathan J Danon, David A Leigh, Jean-François Lemonnier + 1 more
'Jean-François Lemonnier' 'Iñigo J Vitorica-Yrezabal'] A molecular Solomon link was synthesized through the assembly of an interwoven molecular grid consisting of four bis(benzimidazolepyridyl)benzthiazolo[5,4-d]thiazole ligands and four zinc(II), iron(II), or cobalt(II) cations, followed by ring-closing olefin…
Jonathon E Beves, Christopher J Campbell, David A Leigh, Robin G Pritchard
A Solomon link, colloquially termed a “Solomon knot” (a link in Alexander-Briggs notation), is a topology of two interwoven rings that cross each other four times in the simplest representation (Figure [fig01]). Such doubly-entwined catenanes are still rare,[-] with only two small-molecule examples with wholly organic…
Zhicheng Wang, Sahil Kulkarni, Jia Nong, Marco Zamora + 16 more
When a material enters the body, it is immediately attacked by hundreds of proteins, organized into complex networks of binding interactions and reactions. How do such complex systems interact with a material, “deciding” whether to attack? We focus on the “complement” system of ∼40 blood proteins that bind microbes…
Caitlin Randolph, Connor Beveridge, Sanjay Iyer, Stephen Blanksby + 2 more
While various mass spectrometric approaches have been applied to lipid analysis, unraveling the extensive structural diversity of lipids remains a significant challenge. Notably, these approaches often fail to differentiate between isomeric lipids - a challenge that is particularly acute for branched-chain fatty acids…