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DNA, Knots and Tangles

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The Mathematics of Knots

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 1))

Abstract

The DNA of all organisms has a complex and essential topology. Each cell has a family of naturally occurring enzymes that manipulate cellular DNA in topologically interesting and non-trivial ways in order to mediate the vital cellular life processes of replication, transcription and recombination. In order to assay enzyme binding and mechanism, molecular biologists developed the topological approach to enzymology, an experimental protocol in which one reacts small artificial circular DNA substrate molecules with purified enzyme in vitro (in the test tube). The enzyme acts on the DNA substrate, causing changes in the geometry (supercoiling) and/or topology (knotting and linking) of the DNA molecules. Once change in topology of the DNA is known, mathematical analysis can be employed to tease out the structure of the active DNA-protein complex and the changes in that structure due to enzyme mechanism. This paper will describe the tangle model and apply it to the case of site-specific DNA recombination.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    De Witt Sumners

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  1. De Witt Sumners
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Correspondence to De Witt Sumners .

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  1. Department of Mathematics, University of Heidelberg, Im Neuenheimer Feld 288, Heidelberg, 69120, Germany

    Markus Banagl

  2. Department of Mathematics, University of Heidelberg, Im Neuenheimer Feld 288, Heidelberg, 69120, Germany

    Denis Vogel

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Sumners, D.W. (2011). DNA, Knots and Tangles. In: Banagl, M., Vogel, D. (eds) The Mathematics of Knots. Contributions in Mathematical and Computational Sciences, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15637-3_11

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