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Direct observation of DNA knots using a solid-state nanopore

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Abstract

Long DNA molecules can self-entangle into knots. Experimental techniques for observing such DNA knots (primarily gel electrophoresis) are limited to bulk methods and circular molecules below 10 kilobase pairs in length. Here, we show that solid-state nanopores can be used to directly observe individual knots in both linear and circular single DNA molecules of arbitrary length. The DNA knots are observed as short spikes in the nanopore current traces of the traversing DNA molecules and their detection is dependent on a sufficiently high measurement resolution, which can be achieved using high-concentration LiCl buffers. We study the percentage of molecules with knots for DNA molecules of up to 166 kilobase pairs in length and find that the knotting occurrence rises with the length of the DNA molecule, consistent with a constant knotting probability per unit length. Our experimental data compare favourably with previous simulation-based predictions for long polymers. From the translocation time of the knot through the nanopore, we estimate that the majority of the DNA knots are tight, with remarkably small sizes below 100 nm. In the case of linear molecules, we also observe that knots are able to slide out on application of high driving forces (voltage).

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Figure 1: A schematic illustration of a DNA molecule with a knot translocating through a solid-state nanopore.
Figure 2: Six example events for lambda DNA translocating through a 10 nm pore at 200 mV in 2 M LiCl at 30 kHz bandwidth.
Figure 3: Percentage of events with knots as a function of DNA length.
Figure 4: Normalized centre position of knots observed in 20.7 kbp relaxed circular molecules.
Figure 5: Translocation duration of knots (τ) observed in 20.7 kbp linear molecules in 4 M LiCl at 100 mV.

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References

  1. Sumners, D. W. & Whittington, S. G. Knots in self-avoiding walks. J. Phys. A 21, 1689–1694 (1988).

    Article  Google Scholar 

  2. Kawauchi, A. Survey on Knot Theory (Springer, 1996).

    Google Scholar 

  3. Meluzzi, D., Smith, D. E. & Arya, G. Biophysics of knotting. Annu. Rev. Biophys. 39, 349–366 (2010).

    Article  CAS  Google Scholar 

  4. Staczek, P. & Higgins, N. P. Gyrase and Topo IV modulate chromosome domain size in vivo. Mol. Microbiol. 29, 1435–1448 (1998).

    Article  CAS  Google Scholar 

  5. Rodríguez-Campos, A. DNA knotting abolishes in vitro chromatin assembly. J. Biol. Chem. 271, 14150–14155 (1996).

    Article  Google Scholar 

  6. Portugal, J. & Rodríguez-Campos, A. T7 RNA polymerase cannot transcribe through a highly knotted DNA template. Nucleic Acids Res. 24, 4890–4894 (1996).

    Article  CAS  Google Scholar 

  7. Grosberg, A. Y. A few notes about polymer knots. Polymer Sci. Ser. A 51, 70–79 (2009).

    Article  Google Scholar 

  8. Metzler, R. et al. Equilibrium shapes of flat knots. Phys. Rev. Lett. 88, 188101 (2002).

    Article  Google Scholar 

  9. Orlandini, E., Stella, A. L. & Vanderzande, C. The size of knots in polymers. Phys. Biol. 6, 025012 (2009).

    Article  Google Scholar 

  10. Grosberg, A. Y. & Rabin, Y. Metastable tight knots in a wormlike polymer. Phys. Rev. Lett. 99, 217801 (2007).

    Article  Google Scholar 

  11. Tang, J., Du, N. & Doyle, P. S. Compression and self-entanglement of single DNA molecules under uniform electric field. Proc. Natl Acad. Sci. USA 108, 16153–16158 (2011).

    Article  CAS  Google Scholar 

  12. Bao, X. R., Lee, H. J. & Quake, S. R. Behavior of complex knots in single DNA molecules. Phys. Rev. Lett. 91, 265506 (2003).

    Article  Google Scholar 

  13. Arai, Y. et al. Tying a molecular knot with optical tweezers. Nature 399, 446–448 (1999).

    Article  CAS  Google Scholar 

  14. Krasnow, M. A. et al. Determination of the absolute handedness of knots and catenanes of DNA. Nature 304, 559–560 (1983).

    Article  CAS  Google Scholar 

  15. Liu, L. F., Davis, J. L. & Calendar, R. Novel topologically knotted DNA from bacteriophage P4 capsids: studies with DNA topoisomerases. Nucleic Acids Res. 9, 3979–3989 (1981).

    Article  CAS  Google Scholar 

  16. Trigueros, S. et al. Novel display of knotted DNA molecules by two-dimensional gel electrophoresis. Nucleic Acids Res. 29, e67–e67 (2001).

    Article  CAS  Google Scholar 

  17. Wasserman, S. A., Dungan, J. M. & Cozzarelli, N. R. Discovery of a predicted DNA knot substantiates a model for site-specific recombination. Science 229, 171–174 (1985).

    Article  CAS  Google Scholar 

  18. Rybenkov, V. V., Cozzarelli, N. R. & Vologodskii, A. V. Probability of DNA knotting and the effective diameter of the DNA double helix. Proc. Natl Acad. Sci. USA 90, 5307–5311 (1993).

    Article  CAS  Google Scholar 

  19. Shaw, S. Y. & Wang, J. C. Knotting of a DNA chain during ring closure. Science 260, 533–536 (1993).

    Article  CAS  Google Scholar 

  20. Ercolini, E. et al. Fractal dimension and localization of DNA knots. Phys. Rev. Lett. 98, 058102 (2007).

    Article  Google Scholar 

  21. Wasserman, S. A. & Cozzarelli, N. R. Biochemical topology: applications to DNA recombination and replication. Science 232, 951–960 (1986).

    Article  CAS  Google Scholar 

  22. Haque, F. et al. Solid-state and biological nanopore for real-time sensing of single chemical and sequencing of DNA. Nano Today 8, 56–74 (2013).

    Article  CAS  Google Scholar 

  23. Wanunu, M. Nanopores: a journey towards DNA sequencing. Phys. Life Rev. 9, 125–158 (2012).

    Article  Google Scholar 

  24. Muthukumar, M. Mechanism of DNA transport through pores. Annu. Rev. Biophys. Biomol. Struct. 36, 435–450 (2007).

    Article  CAS  Google Scholar 

  25. Storm, A. J. et al. Fast DNA translocation through a solid-state nanopore. Nano Lett. 5, 1193–1197 (2005).

    Article  CAS  Google Scholar 

  26. Plesa, C., Cornelissen, L., Tuijtel, M. W. & Dekker, C. Non-equilibrium folding of individual DNA molecules recaptured up to 1000 times in a solid state nanopore. Nanotechnology 24, 475101 (2013).

    Article  Google Scholar 

  27. Gershow, M. & Golovchenko, J. A. Recapturing and trapping single molecules with a solid-state nanopore. Nature Nanotech. 2, 775–779 (2007).

    Article  CAS  Google Scholar 

  28. Mihovilovic, M., Hagerty, N. & Stein, D. Statistics of DNA capture by a solid-state nanopore. Phys. Rev. Lett. 110, 028102 (2013).

    Article  Google Scholar 

  29. Kantor, Y. & Kardar, M. Anomalous dynamics of forced translocation. Phys. Rev. E 69, 021806 (2004).

    Article  Google Scholar 

  30. Rosa, A., Di Ventra, M. & Micheletti, C. Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore. Phys. Rev. Lett. 109, 118301 (2012).

    Article  CAS  Google Scholar 

  31. Huang, L. & Makarov, D. E. Translocation of a knotted polypeptide through a pore. J. Chem. Phys. 129, 121107 (2008).

    Article  Google Scholar 

  32. Suma, A., Rosa, A. & Micheletti, C. Pore translocation of knotted polymer chains: how friction depends on knot complexity. ACS Macro Lett. 4, 1420–1424 (2015).

    Article  CAS  Google Scholar 

  33. Rieger, F. C. & Virnau, P. A Monte Carlo study of knots in long double-stranded DNA chains. PLoS Comput. Biol. http://dx.doi.org/10.1371/journal.pcbi.1005029 (2016).

  34. Ando, G., Hyun, C., Li, J. & Mitsui, T. Directly observing the motion of DNA molecules near solid-state nanopores. ACS Nano 6, 10090–10097 (2012).

    Article  CAS  Google Scholar 

  35. Deguchi, T. & Tsurusaki, K. A statistical study of random knotting using the Vassiliev invariants. J. Knot Theor. Ramif. 03, 321–353 (1994).

    Article  Google Scholar 

  36. Kowalczyk, S. W., Wells, D. B., Aksimentiev, A. & Dekker, C. Slowing down DNA translocation through a nanopore in lithium chloride. Nano Lett. 12, 1038–1044 (2012).

    Article  CAS  Google Scholar 

  37. Vologodskii, A. Brownian dynamics simulation of knot diffusion along a stretched DNA molecule. Biophys. J. 90, 1594–1597 (2006).

    Article  CAS  Google Scholar 

  38. Wang, J. C. & Davidson, N. Thermodynamic and kinetic studies on the interconversion between the linear and circular forms of phage lambda DNA. J. Mol. Biol. 15, 111–123 (1966).

    Article  CAS  Google Scholar 

  39. Carlsen, A. T. et al. Interpreting the conductance blockades of DNA translocations through solid-state nanopores. ACS Nano 8, 4754–4760 (2014).

    Article  CAS  Google Scholar 

  40. Rosenstein, J. K. et al. Integrated nanopore sensing platform with sub-microsecond temporal resolution. Nature Methods 9, 487–492 (2012).

    Article  CAS  Google Scholar 

  41. Kowalczyk, S. W. & Dekker, C. Measurement of the docking time of a DNA molecule onto a solid-state nanopore. Nano Lett. 12, 4159–4163 (2012).

    Article  CAS  Google Scholar 

  42. Plesa, C. et al. Velocity of DNA during translocation through a solid state nanopore. Nano Lett. 15, 732–737 (2015).

    Article  CAS  Google Scholar 

  43. Lu, B., Albertorio, F., Hoogerheide, D. P. & Golovchenko, J. A. Origins and consequences of velocity fluctuations during DNA passage through a nanopore. Biophys. J. 101, 70–79 (2011).

    Article  CAS  Google Scholar 

  44. Dai, L., Renner, C. B. & Doyle, P. S. Metastable tight knots in semiflexible chains. Macromolecules 47, 6135–6140 (2014).

    Article  CAS  Google Scholar 

  45. Plesa, C. et al. Fast translocation of proteins through solid state nanopores. Nano Lett. 13, 658–663 (2013).

    Article  CAS  Google Scholar 

  46. Deibler, R. W., Rahmati, S. & Zechiedrich, E. L. Topoisomerase IV, alone, unknots DNA in E. coli. Genes Dev. 15, 748–761 (2001).

    Article  CAS  Google Scholar 

  47. Plesa, C., Ruitenberg, J. W., Witteveen, M. J. & Dekker, C. Detection of individual proteins bound along DNA using solid-state nanopores. Nano Lett. 15, 3153–3158 (2015).

    Article  CAS  Google Scholar 

  48. Janssen, X. J. A. et al. Rapid manufacturing of low-noise membranes for nanopore sensors by trans-chip illumination lithography. Nanotechnology 23, 475302 (2012).

    Article  Google Scholar 

  49. Plesa, C. & Dekker, C. Data analysis methods for solid-state nanopores. Nanotechnology 26, 084003 (2015).

    Article  CAS  Google Scholar 

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Acknowledgements

The authors would like to thank C. Micheletti, M. Di Stefano and P. Virnau for discussions, M.-Y. Wu for TEM drilling of nanopores and R. Joseph and S. W. Kowalczyk for early experiments. This work was supported by the Netherlands Organisation for Scientific Research (NWO/OCW), as part of the Frontiers of Nanoscience program, and by the European Research Council under research grant NanoforBio (no. 247072) and SynDiv (no. 669598), the Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) Academy Assistants Program and by the Wenner-Gren Foundations. Y.R. and A.Y.G. would like to acknowledge support from the US–Israel Binational Science foundation.

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C.P., D.V., S.P., J.v.d.T., J.W.R, M.J.W. and M.P.J. carried out the measurements; C.P. and D.V. analysed experimental data; A.Y.G. and Y.R. provided theoretical interpretation; all authors discussed and interpreted results; C.P. and C.D. wrote the manuscript with input from all authors.

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Correspondence to Cees Dekker.

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Plesa, C., Verschueren, D., Pud, S. et al. Direct observation of DNA knots using a solid-state nanopore. Nature Nanotech 11, 1093–1097 (2016). https://doi.org/10.1038/nnano.2016.153

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