Circuit Topology for Bottom-Up Engineering of Molecular Knots
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2353 |
| _version_ | 1797500303861350400 |
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| author | Anatoly Golovnev Alireza Mashaghi |
| author_facet | Anatoly Golovnev Alireza Mashaghi |
| author_sort | Anatoly Golovnev |
| collection | DOAJ |
| description | The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide them with thermal and kinetic stability. Yet, little is known about the design principles of naturally evolved molecular knots. Intra-chain contacts and chain entanglement contribute to the folding of knotted proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized to account for chain entanglement. This generalization is unique to circuit topology and not motivated by other theories. In this conceptual paper, we systematically analyze the circuit topology approach to a description of linear chain entanglement. We utilize a bottom-up approach, i.e., we express entanglement by a set of four fundamental structural units subjected to three (or five) binary topological operations. All knots found in proteins form a well-defined, distinct group which naturally appears if expressed in terms of these basic structural units. We believe that such a detailed, bottom-up understanding of the structure of molecular knots should be beneficial for molecular engineering. |
| first_indexed | 2024-03-10T03:59:58Z |
| format | Article |
| id | doaj.art-663f26504c8d44ffae2e212db9e5c388 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:59:58Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-663f26504c8d44ffae2e212db9e5c3882023-11-23T10:45:56ZengMDPI AGSymmetry2073-89942021-12-011312235310.3390/sym13122353Circuit Topology for Bottom-Up Engineering of Molecular KnotsAnatoly Golovnev0Alireza Mashaghi1Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Einsteinweg 55, 2333 CC Leiden, The NetherlandsMedical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Einsteinweg 55, 2333 CC Leiden, The NetherlandsThe art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide them with thermal and kinetic stability. Yet, little is known about the design principles of naturally evolved molecular knots. Intra-chain contacts and chain entanglement contribute to the folding of knotted proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized to account for chain entanglement. This generalization is unique to circuit topology and not motivated by other theories. In this conceptual paper, we systematically analyze the circuit topology approach to a description of linear chain entanglement. We utilize a bottom-up approach, i.e., we express entanglement by a set of four fundamental structural units subjected to three (or five) binary topological operations. All knots found in proteins form a well-defined, distinct group which naturally appears if expressed in terms of these basic structural units. We believe that such a detailed, bottom-up understanding of the structure of molecular knots should be beneficial for molecular engineering.https://www.mdpi.com/2073-8994/13/12/2353circuit topologyknot theoryfoldingpolymer |
| spellingShingle | Anatoly Golovnev Alireza Mashaghi Circuit Topology for Bottom-Up Engineering of Molecular Knots Symmetry circuit topology knot theory folding polymer |
| title | Circuit Topology for Bottom-Up Engineering of Molecular Knots |
| title_full | Circuit Topology for Bottom-Up Engineering of Molecular Knots |
| title_fullStr | Circuit Topology for Bottom-Up Engineering of Molecular Knots |
| title_full_unstemmed | Circuit Topology for Bottom-Up Engineering of Molecular Knots |
| title_short | Circuit Topology for Bottom-Up Engineering of Molecular Knots |
| title_sort | circuit topology for bottom up engineering of molecular knots |
| topic | circuit topology knot theory folding polymer |
| url | https://www.mdpi.com/2073-8994/13/12/2353 |
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