{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:43:34Z","timestamp":1766486614705,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:00:00Z","timestamp":1631232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N509711\/1","EP\/R018472\/1","EP\/N510129\/1"],"award-info":[{"award-number":["EP\/N509711\/1","EP\/R018472\/1","EP\/N510129\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hooke Fellowship","award":["NA"],"award-info":[{"award-number":["NA"]}]},{"DOI":"10.13039\/501100000921","name":"European Cooperation in Science and Technology","doi-asserted-by":"publisher","award":["CA17139"],"award-info":[{"award-number":["CA17139"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins\u2019 native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.<\/jats:p>","DOI":"10.3390\/sym13091670","type":"journal-article","created":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T21:48:01Z","timestamp":1631483281000},"page":"1670","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Topological Selection of Folding Pathways from Native States of Knotted Proteins"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9348-4478","authenticated-orcid":false,"given":"Agnese","family":"Barbensi","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3718-7270","authenticated-orcid":false,"given":"Naya","family":"Yerolemou","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK"},{"name":"The Alan Turing Institute, London NW1 2DB, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2355-5570","authenticated-orcid":false,"given":"Oliver","family":"Vipond","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4693-1420","authenticated-orcid":false,"given":"Barbara I.","family":"Mahler","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9412-1716","authenticated-orcid":false,"given":"Pawel","family":"Dabrowski-Tumanski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Natural Sciences, School of Exact Sciences, Cardinal Stefan Wyszynski University, Woycickiego 1\/3, 01-938 Warsaw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2874-6272","authenticated-orcid":false,"given":"Dimos","family":"Goundaroulis","sequence":"additional","affiliation":[{"name":"The Center for Genome Architecture, Baylor College of Medicine, Houston, TX 77030, USA"},{"name":"Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, TX 77030, USA"},{"name":"Center for Theoretical Biological Physics, Rice University, Houston, TX 77030, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"D301","DOI":"10.1093\/nar\/gkl971","article-title":"The worldwide Protein Data Bank (wwPDB): Ensuring a single, uniform archive of PDB data","volume":"35","author":"Berman","year":"2007","journal-title":"Nucleic Acids Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"D367","DOI":"10.1093\/nar\/gky1140","article-title":"KnotProt 2.0: A database of proteins with knots and other entangled structures","volume":"47","author":"Rubach","year":"2019","journal-title":"Nucleic Acids Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3119","DOI":"10.1073\/pnas.0811147106","article-title":"Dodging the crisis of folding proteins with knots","volume":"106","author":"Onuchic","year":"2009","journal-title":"Proc. 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