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Biomechanics in Oncology pp 11–39Cite as

DNA Mechanics and Topology

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Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1092))

Abstract

We review the current understanding of the mechanics of DNA and DNA-protein complexes, from scales of base pairs up to whole chromosomes. Mechanics of the double helix as revealed by single-molecule experiments will be described, with an emphasis on the role of polymer statistical mechanics. We will then discuss how topological constraints— entanglement and supercoiling—impact physical and mechanical responses. Models for protein–DNA interactions, including effects on polymer properties of DNA of DNA-bending proteins will be described, relevant to behavior of protein–DNA complexes in vivo. We also discuss control of DNA entanglement topology by DNA-lengthwise-compaction machinery acting in concert with topoisomerases. Finally, the chapter will conclude with a discussion of relevance of several aspects of physical properties of DNA and chromatin to oncology.

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Notes

  1. 1.

    Linking topology is perfectly well defined only for closed curves or polymers. However, it is sometimes useful to define linkage of open curves, using suitably defined closure boundary conditions, e.g., closing chains at infinity by extending them with long straight paths. This introduces small corrections to the properties of entanglement of interest here (primarily estimates of linking number). Qualitatively this can be understood by considering the definition of linking number in terms of signed crossings (Fig. 2.4). If we imagine deforming part of one of the links of Fig. 2.3 so that it closes far from the other crossings (not introducing any new crossings in the process) the topology and linking number of the polymer will be unchanged. This will be true for all closure paths that do not introduce additional strand crossings, indicating a rather weak dependence of linking number on closure boundary conditions, and further allowing us to talk about the topology of the region of the polymers not including the closure in a reasonably well-defined way. This is particularly true for linking of stretched polymers as will be discussed below; see, e.g., [34].

  2. 2.

    The total twist of a DNA molecule is often written as the excess twist ΔTw plus the intrinsic twist, or Tw = ΔTw + Lk0 = ΔTw + L∕h, where ΔTw = Θ∕(2π).

  3. 3.

    Electrostatic interactions are usually treated using a far-field approximation of the Poisson–Boltzmann equation, where the electrostatic potential is that of the screened-Coulomb type [7, 43].

  4. 4.

    A nick on a DNA means there is a break in one of the strands of the double helix. Nicks act as a “sink” for twist in the molecule via mechanical rotation about the single-stranded region. In other words, nicked DNAs are torsionally unconstrained.

  5. 5.

    Note that the extension curves for nicked DNA braids (Fig. 2.9b) are symmetric for positive and negative catenations, as a virtue of the individual dsDNAs being torsionally unconstrained.

  6. 6.

    In vivo, type II topos may control 〈Ca〉 via selective decatenation, thus driving disentanglement.

  7. 7.

    The shape of the confining volume is an interesting aspect. For tight cylindrical confinement, chains will tend to separate from one another along the cylinder, to minimize their stretching (and therefore to maximize their entropy). This effect has been proposed to play a role in the segregation of bacterial chromosomes in rod-shaped bacteria [87, 88], although folding and compaction of bacterial chromosomes may also play a role in their separation [89].

  8. 8.

    K d is used widely by biochemists; note that the equilibrium constant used widely by chemists is just K eq ≡ 1∕K d.

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Authors and Affiliations

  1. Northwestern University, Evanston, IL, USA

    Sumitabha Brahmachari & John F. Marko

Authors
  1. Sumitabha Brahmachari
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  2. John F. Marko
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Correspondence to John F. Marko .

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Editors and Affiliations

  1. Department of Biomedical Engineering, Pennsylvania State University, University Park, PA, USA

    Cheng Dong

  2. Division of Cancer Biology, National Cancer Institute, National Institutes of Health, Rockville, MD, USA

    Nastaran Zahir

  3. Department of Chemical and Biomolecular Engineering Institute for NanoBioTechnology, Johns Hopkins University, Baltimore, MD, USA

    Konstantinos Konstantopoulos

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Brahmachari, S., Marko, J.F. (2018). DNA Mechanics and Topology. In: Dong, C., Zahir, N., Konstantopoulos, K. (eds) Biomechanics in Oncology. Advances in Experimental Medicine and Biology, vol 1092. Springer, Cham. https://doi.org/10.1007/978-3-319-95294-9_2

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