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Proteins analysed as virtual knots
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. Knott...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5304221/ https://www.ncbi.nlm.nih.gov/pubmed/28205562 http://dx.doi.org/10.1038/srep42300 |
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author | Alexander, Keith Taylor, Alexander J. Dennis, Mark R. |
author_facet | Alexander, Keith Taylor, Alexander J. Dennis, Mark R. |
author_sort | Alexander, Keith |
collection | PubMed |
description | 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 previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important. |
format | Online Article Text |
id | pubmed-5304221 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Nature Publishing Group |
record_format | MEDLINE/PubMed |
spelling | pubmed-53042212017-03-14 Proteins analysed as virtual knots Alexander, Keith Taylor, Alexander J. Dennis, Mark R. Sci Rep Article 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 previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important. Nature Publishing Group 2017-02-13 /pmc/articles/PMC5304221/ /pubmed/28205562 http://dx.doi.org/10.1038/srep42300 Text en Copyright © 2017, The Author(s) http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
spellingShingle | Article Alexander, Keith Taylor, Alexander J. Dennis, Mark R. Proteins analysed as virtual knots |
title | Proteins analysed as virtual knots |
title_full | Proteins analysed as virtual knots |
title_fullStr | Proteins analysed as virtual knots |
title_full_unstemmed | Proteins analysed as virtual knots |
title_short | Proteins analysed as virtual knots |
title_sort | proteins analysed as virtual knots |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5304221/ https://www.ncbi.nlm.nih.gov/pubmed/28205562 http://dx.doi.org/10.1038/srep42300 |
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