The Kauffman bracket skein module of bonded knots and applications to entangled proteins

Gabrovšek, Boštjan (author), Simonič, Matic (author)

We model proteins with intramolecular bonds, such as disulfide bridges, using the concept of bonded knots-closed loops in three-dimensional space equipped with additional bonds that connect different segments of the knot. We extend the Kauffman bracket polynomial (which is closely related to the Jones polynomial) to bonded knots through the introduction of the bonded version of the Kauffman bracket skein module. We show that this module is infinitely generated and torsion-free for both the rigid and topological case of bonded knots. In the rigid case, evaluating a bonded knot in the basis of this module yields an bonded knot invariant closely related to the APS bracket and the Simplified RNA polynomial.

• Language: English
• Keywords: bonded knots, Kauffman bracket, protein knots, skein modules
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics; FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 16 str.
• Numbering: Vol. 155, iss. 5, art. e70123
• PID: 20.500.12556/RUL-175820
• UDC: 515.1
• ISSN on article: 0022-2526
• DOI: 10.1111/sapm.70123
• COBISS.SI-ID: 256501763
• Publication date in RUL: 10.11.2025

Record is a part of a journal

• Title: Studies in applied mathematics
• Shortened title: Stud. appl. math.
• Publisher: Wiley
• ISSN: 0022-2526
• COBISS.SI-ID: 26469376

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.