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Reactions Mediated by Topoisomerases and Other Enzymes: Modelling Localised DNA Transformations

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Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

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Abstract

Many proteins cleave and reseal DNA molecules in precisely orchestrated ways. Modelling these reactions has often relied on the axis of the DNA double helix being circular, so these cut-and-seal mechanisms can be tracked by corresponding changes in the knot type of the DNA axis. However, when the DNA molecule is linear, or the protein action does not manifest itself as a change in knot type, or the knot types are not 4-plats, these knot-theoretic models are less germane. We thus give a taxonomy of local DNA axis configurations. More precisely, we characterise all rational tangles obtained from a given rational tangle via a rational-subtangle replacement. This classification is then endowed biologically with a distance that determines how many enzyme-mediated reactions of a particular type are needed to proceed from one local DNA conformation to another, or indeed if it is even possible. We conclude by discussing a variety of biological applications of this categorisation, including reactions mediated by type II topoisomerase, site-specific recombinase and transposase.

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Acknowledgements

The author would like to express many thanks to Ken Baker, who co-authored the topological proofs that were applied to the biological systems described above, and who provided several of the figures. Thanks also to the reviewers for their careful reading and insightful comments. Also, thanks to the UK’s Engineering and Physical Sciences Research Council, which has generously supported the author through grants EP/H0313671, EP/G0395851 and EP/J1075308, and to the London Mathematical Society, which has supported her research through two LMS Scheme 2 Awards. Finally, much gratitude to Natasha Jonoska, Alessandra Carbone, Katarzyna Rejniak, Masahico Saito and Reidun Twarock for organising the stimulating and enjoyable Discrete and Topological Models in Molecular Biology Conference, as well as for inviting this article.

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  1. Department of Mathematics, Imperial College London, London, UK

    Dorothy Buck

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  1. Dorothy Buck
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Correspondence to Dorothy Buck .

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  1. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

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Buck, D. (2014). Reactions Mediated by Topoisomerases and Other Enzymes: Modelling Localised DNA Transformations. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-40193-0_16

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