Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

Panagiotou, Eleni; Millett, Kenneth C.; Atzberger, Paul J.

doi:10.3390/polym11030437

Cited by 30 publications

(27 citation statements)

References 67 publications

(90 reference statements)

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“…Polymer Entanglements, Tubes, and Knots Panagiotou et al [9] developed topological methods for characterizing the relationship between polymer chain entanglement, knots, and bulk viscoelastic responses. A phenomenon known as "knot-breathing" occurs in biopolymers such as DNA and peptides.…”

Section: Semiflexible Polymersmentioning

confidence: 99%

Developments in Polymer Theory and Simulation

Kröger

2019

Polymers

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Section: Semiflexible Polymersmentioning

confidence: 99%

Developments in Polymer Theory and Simulation

Kröger

2019

Polymers

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“…The Writhe and the Torsion have successfully been applied to study entanglement in biopolymers and proteins in particular [2,6,6–8,17,18,40,43–45,47,49,52].…”

Section: Methodsmentioning

confidence: 99%

The local topological free energy of the SARS-CoV-2 Spike protein

Baldwin

Panagiotou

2021

Preprint

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The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its spike protein. Understanding protein rearrangement and identifying specific residues where mutations affect protein rearrangement has attracted a lot of attention for drug development. We use a mathematical method introduced in (Baldwin2021) to associate a local topological/geometrical free energy along the SARS-CoV-2 spike protein backbone. Our results show that the total local topological free energy of the SARS-CoV-2 spike protein monotonically decreases from pre-to post-fusion and that its distribution along the protein domains is related to their activity in protein rearrangement. By using density functional theory (DFT) calculations with inclusion of solvent effects, we show that high local topological free energy conformations are unstable compared to those of low topological free energy. By comparing to experimental data, we find that the high local topological free energy conformations in the spike protein are associated with mutations which have the largest experimentally observed effect to protein rearrangement.

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“…Our proof-of-concept -the restricted and unrestricted searches -and rar0 make use only of the writhe for identifying locally entangled configurations. Several authors have recently made similar use of the writhe, but for defining a global entanglement of one or more polymers [1] [19] . Closest to our application of the local writhe numbers are [2] [3].…”

Section: Introductionmentioning

confidence: 99%

Peer Review #2 of "GISA: using Gauss Integrals to identify rare conformations in protein structures (v0.1)"

2020

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The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few methods are sensitive to topologicgeometric features, the examples being knots, slipknots, lassos, links, and pokes, and with each method aimed only for a specific set of such configurations. We here propose a general method which transforms a structure into a "fingerprint of topological-geometric values" consisting in a series of real-valued descriptors from mathematical Knot Theory. The extent to which a structure contains unusual configurations can then be judged from this fingerprint. The method is not confined to a particular predefined topology or geometry (like a knot or a poke), and so, unlike existing methods, it is general. To achieve this our new algorithm, GISA, as a key novelty produces the descriptors, so called Gauss integrals, not only for the full chains of a protein but for all its sub-chains. This allows fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds. Applying GISA to sets of several thousand high resolution structures, we first show how the most basic Gauss Integral, the writhe, enables swift identification of pre-defined geometries such as pokes and links. We then apply GISA with no restrictions on geometry, to show how it allows identifying rare conformations by finding rare invariant values only. In this unrestricted search, pokes and links are still found, but also knotted conformations, as well as more highly entangled configurations not previously described. Thus, an application of the basic scan method in GISA's toolbox revealed 10 known cases of knots as the top positive writhe cases, while placing at the top of the negative writhe 14 cases in cistrans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed. Possible general applications of GISA are fold classification and structural alignment based on local Gauss Integrals. Others include finding errors in protein models and identifying unusual conformations that might be important for protein folding and function. By its broad potential, we believe that GISA will be of general benefit to the structural bioinformatics community. GISA is coded in C and comes as a command line tool. Source and compiled code for GISA plus read-me and examples are publicly available at GitHub (https://github.com).

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Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

Cited by 30 publications

References 67 publications

Developments in Polymer Theory and Simulation

Developments in Polymer Theory and Simulation

The local topological free energy of the SARS-CoV-2 Spike protein

Peer Review #2 of "GISA: using Gauss Integrals to identify rare conformations in protein structures (v0.1)"

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