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Genus trace reveals the topological complexity and domain structure of biomolecules

Zając, Sebastian and Geary, Cody and Andersen, Ebbe Sloth and Dabrowski-Tumanski, Pawel and Sulkowska, Joanna I. and Sułkowski, Piotr (2018) Genus trace reveals the topological complexity and domain structure of biomolecules. Scientific Reports, 8 . Art. No. 17537. ISSN 2045-2322. PMCID PMC6277428. doi:10.1038/s41598-018-35557-3.

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The structure of bonds in biomolecules, such as base pairs in RNA chains or native interactions in proteins, can be presented in the form of a chord diagram. A given biomolecule is then characterized by the genus of an auxiliary two-dimensional surface associated to such a diagram. In this work we introduce the notion of the genus trace, which describes dependence of genus on the choice of a subchain of a given backbone chain. We find that the genus trace encodes interesting physical and biological information about a given biomolecule and its three dimensional structural complexity; in particular it gives a way to quantify how much more complicated a biomolecule is than its nested secondary structure alone would indicate. We illustrate this statement in many examples, involving both RNA and protein chains. First, we conduct a survey of all published RNA structures with better than 3 Å resolution in the PDB database, and find that the genus of natural structural RNAs has roughly linear dependence on their length. Then, we show that the genus trace captures properties of various types of base pairs in RNA, and enables the identification of the domain structure of a ribosome. Furthermore, we find that not only does the genus trace detect a domain structure, but it also predicts a cooperative folding pattern in multi-domain proteins. The genus trace turns out to be a useful and versatile tool, with many potential applications.

Item Type:Article
Related URLs:
URLURL TypeDescription CentralArticle
Geary, Cody0000-0003-2083-4259
Andersen, Ebbe Sloth0000-0002-6236-8164
Dabrowski-Tumanski, Pawel0000-0001-9412-1716
Sulkowska, Joanna I.0000-0003-2452-0724
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2018 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit Received 01 May 2018; Accepted 01 November 2018; Published 03 December 2018. We thank Gaja Klaudel for help with preparing the plot of the genus trace for a protein, and Bartłomiej Burek for help with Python. This work is supported by the Foundation for Polish Science and the ERC Starting Grant #335739 “Quantum fields and knot homologies” funded by the European Research Council under the European Union’s Seventh Framework Programme (to PS), the ERC Consolidator Grant #683305 “RNA ORIGAMI: RNA-protein nanostructures for Synthetic Biology” (to ESA), the Carlsberg Research Foundation (to CG), Polish Ministry for Science and Higher Education #0003/ID3/2016/64 grant and National Science Centre grant #2012/07/E/NZ1/01900 (to JIS), and National Science Centre #2016/21/N/NZ1/02848 grant (to PDT). Author Contributions: S.Z., C.G., E.S.A., J.I.S. and P.S. designed the work, S.Z., C.G., E.S.A., P.D.-T., J.I.S. and P.S. performed the work, C.G., P.D.-T., J.I.S. and P.S. wrote the paper. The authors declare no competing interests.
Funding AgencyGrant Number
Foundation for Polish ScienceUNSPECIFIED
European Research Council (ERC)335739
European Research Council (ERC)683305
Carlsberg Research FoundationUNSPECIFIED
Ministerstwo Nauki i Szkolnictwa Wyższego (MNiSW)0003/ID3/2016/64
National Science Centre (Poland)2012/07/E/NZ1/01900
National Science Centre (Poland)2016/21/N/NZ1/02848
PubMed Central ID:PMC6277428
Record Number:CaltechAUTHORS:20181210-073729134
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91636
Deposited By: Tony Diaz
Deposited On:10 Dec 2018 19:45
Last Modified:02 Mar 2022 00:15

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