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Pathways of DNA unlinking: A story of stepwise simplification

Robert Stolz, Masaaki Yoshida, Reuben Brasher, Michelle Flanner, Kai Ishihara, David J. Sherratt, Koya Shimokawa, Mariel Vazquez
doi: https://doi.org/10.1101/188722
Robert Stolz
1Department of Microbiology and Molecular Genetics, University of California Davis, Davis, USA
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Masaaki Yoshida
2Department of Mathematics, Saitama University, Saitama, Japan
7Takasaki City Office, 35-1 Takamatsu-cho, Takasaki, Japan
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Reuben Brasher
3Microsoft, San Francisco, USA
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Michelle Flanner
1Department of Microbiology and Molecular Genetics, University of California Davis, Davis, USA
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Kai Ishihara
4Faculty of Education, Yamaguchi University, Yamaguchi, Japan
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David J. Sherratt
5Department of Biochemistry, University of Oxford, Oxford, UK
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Koya Shimokawa
2Department of Mathematics, Saitama University, Saitama, Japan
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Mariel Vazquez
1Department of Microbiology and Molecular Genetics, University of California Davis, Davis, USA
6Department of Mathematics, University of California Davis, Davis, USA
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Abstract

In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD-dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted September 14, 2017.
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Pathways of DNA unlinking: A story of stepwise simplification
Robert Stolz, Masaaki Yoshida, Reuben Brasher, Michelle Flanner, Kai Ishihara, David J. Sherratt, Koya Shimokawa, Mariel Vazquez
bioRxiv 188722; doi: https://doi.org/10.1101/188722
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Pathways of DNA unlinking: A story of stepwise simplification
Robert Stolz, Masaaki Yoshida, Reuben Brasher, Michelle Flanner, Kai Ishihara, David J. Sherratt, Koya Shimokawa, Mariel Vazquez
bioRxiv 188722; doi: https://doi.org/10.1101/188722

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