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Regulation of DNA Topology by Topoisomerases: Mathematics at the Molecular Level

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Knots, Low-Dimensional Topology and Applications (KNOTS16 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 284))

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Abstract

Although the genetic information is encoded in a one-dimensional array of nucleic acid bases, three-dimensional relationships within DNA play a major role in how this information is accessed and utilized by living organisms. Because of the intertwined nature of the DNA two-braid and its extreme length and compaction in the cell, some of the most important three-dimensional relationships in DNA are topological in nature. Topological linkages within the two-braid and between different DNA segments can be described in simple mathematical terms that account for both the twist and the writhe in the double helix. Topoisomerases are ubiquitous enzymes that regulate the topological state of the genetic material by altering either twist or writhe. To do so, these enzymes transiently open the topological system by breaking one or both strands of the two-braid. This article will review the mathematics of DNA topology, describe the different classes of topoisomerases, and discuss the mechanistic basis for their actions in both biological and mathematical terms. Finally, it will discuss how topoisomerases recognize the topological states of their DNA substrates and products and how some of these enzymes distinguish supercoil handedness during catalysis and DNA cleavage. These latter characteristics make topoisomerases well suited for their individual physiological tasks and impact their roles as targets of important anticancer and antibacterial drugs.

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Acknowledgements

Work in the senior author’s laboratory was supported by National Institutes of Health grants R01 GM033944 and R01 GM126363 and US Veterans Administration Merit Review award I01 Bx002198. R.E.A. was supported by pre-doctoral fellowship DGE-0909667 from the National Science Foundation. We are grateful to Elizabeth G. Gibson for critical reading of the manuscript.

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Authors and Affiliations

  1. Vanderbilt University School of Medicine, Nashville, TN, 37232-0146, USA

    Rachel E. Ashley & Neil Osheroff

  2. VA Tennessee Valley Healthcare System, Nashville, TN, 37212, USA

    Neil Osheroff

Authors
  1. Rachel E. Ashley
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  2. Neil Osheroff
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Correspondence to Neil Osheroff .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Williams College, Williamstown, MA, USA

    Colin C. Adams

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

    Cameron McA. Gordon

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, USA

    Vaughan F.R. Jones

  4. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, USA

    Louis H. Kauffman

  5. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  6. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Kenneth C. Millett

  7. Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, DC, USA

    Jozef H. Przytycki

  8. Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

    Renzo Ricca

  9. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Radmila Sazdanovic

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Ashley, R.E., Osheroff, N. (2019). Regulation of DNA Topology by Topoisomerases: Mathematics at the Molecular Level. In: Adams, C., et al. Knots, Low-Dimensional Topology and Applications. KNOTS16 2016. Springer Proceedings in Mathematics & Statistics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-16031-9_20

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