Circuit topology

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From Wikipedia, the free encyclopedia
This article is about the topology of polymers. For the topology of electrical circuits, see Circuit
topology (electrical).
Circuit topology relations in a chain with two binary contacts.
The circuit topology of a folded linear polymer refers to the arrangement of its intra-molecular
contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins.
Proteins fold via the formation of contacts of various natures, including hydrogen bonds, disulfide
bonds, and beta-beta interactions.[1] RNA molecules fold by forming hydrogen bonds between
nucleotides, forming nested or non-nested structures. Contacts in the genome are established via
protein bridges including CTCF and cohesins and are measured by technologies including Hi-C.[2]
Circuit topology categorises the topological arrangement of these physical contacts, that are referred
to as hard contacts (or h-contacts). Furthermore, chains can fold via knotting (or the formation of
"soft" contacts (s-contacts)). Circuit topology uses a similar language to categorise both "soft" and
"hard" contacts, and provides a full description of a folded linear chain. In this framework, a "circuit"
refers to a segment of the chain where each contact site within the segment forms connections with
other contact sites within the same segment, and thus is not left unpaired. A folded chain can thus be
studied based on its constituting circuits.

A simple example of a folded chain is a chain with two hard contacts. For a chain with two binary
contacts, three arrangements are available: parallel (P), series (S), and crossed (X). For a chain with n
contacts, the topology can be described by an n by n matrix in which each element illustrates the
relation between a pair of contacts and may take one of the three states, P, S and X. Multivalent
contacts can also be categorised in full or via decomposition into several binary contacts. Similarly,
circuit topology allows for the classification of the pairwise arrangements of chain crossings and
tangles, thus providing a complete 3D description of folded chains. Furthermore, one can apply circuit
topology operations to soft and hard contacts to generate complex folds, using a bottom-up
engineering approach.
Both knot theory and circuit topology aim to describe chain entanglement, making it important to
understand their relationship. Knot theory considers any entangled chain as a connected sum of
prime knots, which are themselves undecomposable. Circuit topology splits any entangled chains
(including prime knots) into basic structural units called soft contacts, and lists simple rules on how
soft contacts can be put together.[3][4] An advantage of circuit topology is that it can be applied to
open linear chains with intra-chain interactions, so-called hard contacts.[5] This enabled topological
analysis of proteins and genomes, which are often described as "unknot" in knot theory. [6][7] Finally,
circuit topology enables studying interactions between hard contacts and entanglements and can
identify slip knots, while knot theory typically overlooks hard contacts and split knots. Thus, circuit
topology serves as a complementary approach to knot theory.

Circuit topology has implications for folding kinetics and molecular evolution and has been applied to
engineer polymers including molecular origami.[8] Circuit topology along with contact order and size
are determinants of the folding rate of linear polymers.[9] The approach can also be used for medical
applications including the prediction of pathogenicity of mutations.

Further reading
Scalvini, Barbara; Sheikhhassani, Vahid; Mashaghi, Alireza (2021). "Topological principles of protein
folding". Physical Chemistry Chemical Physics. 23 (37): 21316–21328. Bibcode:2021PCCP...2321316S.
doi:10.1039/D1CP03390E. hdl:1887/3277889. PMID 34545868. S2CID 237583577.
Golovnev, Anatoly; Mashaghi, Alireza (September 2020). "Generalized Circuit Topology of Folded
Linear Chains". iScience. 23 (9): 101492. Bibcode:2020iSci...23j1492G. doi:10.1016/j.isci.2020.101492.
PMC 7481252. PMID 32896769.
Heidari, Maziar; Schiessel, Helmut; Mashaghi, Alireza (24 June 2020). "Circuit Topology Analysis of
Polymer Folding Reactions". ACS Central Science. 6 (6): 839–847. doi:10.1021/acscentsci.0c00308.
PMC 7318069. PMID 32607431.
References
Mashaghi, Alireza; van Wijk, Roeland J.; Tans, Sander J. (2014). "Circuit Topology of Proteins and
Nucleic Acids". Structure. 22 (9): 1227–1237. doi:10.1016/j.str.2014.06.015. PMID 25126961.
Scalvini, Barbara; Schiessel, Helmut; Golovnev, Anatoly; Mashaghi, Alireza (March 2022). "Circuit
topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and
scaling". iScience. 25 (3): 103866. Bibcode:2022iSci...25j3866S. doi:10.1016/j.isci.2022.103866. PMC
8861635. PMID 35243229.
Golovnev, Anatoly; Mashaghi, Alireza (7 December 2021). "Circuit Topology for Bottom-Up
Engineering of Molecular Knots". Symmetry. 13 (12): 2353. arXiv:2106.03925.
Bibcode:2021Symm...13.2353G. doi:10.3390/sym13122353.
Flapan, Erica; Mashaghi, Alireza; Wong, Helen (1 June 2023). "A tile model of circuit topology for self-
entangled biopolymers". Scientific Reports. 13 (1): 8889. Bibcode:2023NatSR..13.8889F.
doi:10.1038/s41598-023-35771-8. PMC 10235088. PMID 37264056. S2CID 259022790.
Golovnev, Anatoly; Mashaghi, Alireza (September 2020). "Generalized Circuit Topology of Folded
Linear Chains". iScience. 23 (9): 101492. Bibcode:2020iSci...23j1492G. doi:10.1016/j.isci.2020.101492.
PMC 7481252. PMID 32896769.
Yasuyuki Tezuka, Tetsuo Deguchi, Topological Polymer Chemistry: Concepts and Practices (2022) ISBN
978-981-16-6807-4
"Leiden scientists develop topological barcodes for folded molecules" (Press release). Leiden
University. 25 August 2020.
Yasuyuki Tezuka and Tetsuo Deguchi, Topological Polymer Chemistry: Concepts and Practices (2022)
ISBN 978-981-16-6806-7
Mugler, Andrew; Tans, Sander J.; Mashaghi, Alireza (2014). "Circuit topology of self-interacting
chains: implications for folding and unfolding dynamics". Phys. Chem. Chem. Phys. 16 (41): 22537–
22544. Bibcode:2014PCCP...1622537M. doi:10.1039/C4CP03402C. PMID 25228051.
See also
Molecular topology
Categories: TopologyMolecular topologyMolecular geometryMathematical chemistrySupramolecular
chemistryKnot theoryStructural bioinformatics
This page was last edited on 18 June 2024, at 22:06 (UTC).
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