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).
This is a preview of subscription content, access via your institution
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Sumners, D. W. & Whittington, S. G. Knots in self-avoiding walks. J. Phys. A 21, 1689–1694 (1988).
Kawauchi, A. Survey on Knot Theory (Springer, 1996).
Meluzzi, D., Smith, D. E. & Arya, G. Biophysics of knotting. Annu. Rev. Biophys. 39, 349–366 (2010).
Staczek, P. & Higgins, N. P. Gyrase and Topo IV modulate chromosome domain size in vivo. Mol. Microbiol. 29, 1435–1448 (1998).
Rodríguez-Campos, A. DNA knotting abolishes in vitro chromatin assembly. J. Biol. Chem. 271, 14150–14155 (1996).
Portugal, J. & Rodríguez-Campos, A. T7 RNA polymerase cannot transcribe through a highly knotted DNA template. Nucleic Acids Res. 24, 4890–4894 (1996).
Grosberg, A. Y. A few notes about polymer knots. Polymer Sci. Ser. A 51, 70–79 (2009).
Metzler, R. et al. Equilibrium shapes of flat knots. Phys. Rev. Lett. 88, 188101 (2002).
Orlandini, E., Stella, A. L. & Vanderzande, C. The size of knots in polymers. Phys. Biol. 6, 025012 (2009).
Grosberg, A. Y. & Rabin, Y. Metastable tight knots in a wormlike polymer. Phys. Rev. Lett. 99, 217801 (2007).
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).
Bao, X. R., Lee, H. J. & Quake, S. R. Behavior of complex knots in single DNA molecules. Phys. Rev. Lett. 91, 265506 (2003).
Arai, Y. et al. Tying a molecular knot with optical tweezers. Nature 399, 446–448 (1999).
Krasnow, M. A. et al. Determination of the absolute handedness of knots and catenanes of DNA. Nature 304, 559–560 (1983).
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).
Trigueros, S. et al. Novel display of knotted DNA molecules by two-dimensional gel electrophoresis. Nucleic Acids Res. 29, e67–e67 (2001).
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).
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).
Shaw, S. Y. & Wang, J. C. Knotting of a DNA chain during ring closure. Science 260, 533–536 (1993).
Ercolini, E. et al. Fractal dimension and localization of DNA knots. Phys. Rev. Lett. 98, 058102 (2007).
Wasserman, S. A. & Cozzarelli, N. R. Biochemical topology: applications to DNA recombination and replication. Science 232, 951–960 (1986).
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).
Wanunu, M. Nanopores: a journey towards DNA sequencing. Phys. Life Rev. 9, 125–158 (2012).
Muthukumar, M. Mechanism of DNA transport through pores. Annu. Rev. Biophys. Biomol. Struct. 36, 435–450 (2007).
Storm, A. J. et al. Fast DNA translocation through a solid-state nanopore. Nano Lett. 5, 1193–1197 (2005).
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).
Gershow, M. & Golovchenko, J. A. Recapturing and trapping single molecules with a solid-state nanopore. Nature Nanotech. 2, 775–779 (2007).
Mihovilovic, M., Hagerty, N. & Stein, D. Statistics of DNA capture by a solid-state nanopore. Phys. Rev. Lett. 110, 028102 (2013).
Kantor, Y. & Kardar, M. Anomalous dynamics of forced translocation. Phys. Rev. E 69, 021806 (2004).
Rosa, A., Di Ventra, M. & Micheletti, C. Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore. Phys. Rev. Lett. 109, 118301 (2012).
Huang, L. & Makarov, D. E. Translocation of a knotted polypeptide through a pore. J. Chem. Phys. 129, 121107 (2008).
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).
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).
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).
Deguchi, T. & Tsurusaki, K. A statistical study of random knotting using the Vassiliev invariants. J. Knot Theor. Ramif. 03, 321–353 (1994).
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).
Vologodskii, A. Brownian dynamics simulation of knot diffusion along a stretched DNA molecule. Biophys. J. 90, 1594–1597 (2006).
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).
Carlsen, A. T. et al. Interpreting the conductance blockades of DNA translocations through solid-state nanopores. ACS Nano 8, 4754–4760 (2014).
Rosenstein, J. K. et al. Integrated nanopore sensing platform with sub-microsecond temporal resolution. Nature Methods 9, 487–492 (2012).
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).
Plesa, C. et al. Velocity of DNA during translocation through a solid state nanopore. Nano Lett. 15, 732–737 (2015).
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).
Dai, L., Renner, C. B. & Doyle, P. S. Metastable tight knots in semiflexible chains. Macromolecules 47, 6135–6140 (2014).
Plesa, C. et al. Fast translocation of proteins through solid state nanopores. Nano Lett. 13, 658–663 (2013).
Deibler, R. W., Rahmati, S. & Zechiedrich, E. L. Topoisomerase IV, alone, unknots DNA in E. coli. Genes Dev. 15, 748–761 (2001).
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).
Janssen, X. J. A. et al. Rapid manufacturing of low-noise membranes for nanopore sensors by trans-chip illumination lithography. Nanotechnology 23, 475302 (2012).
Plesa, C. & Dekker, C. Data analysis methods for solid-state nanopores. Nanotechnology 26, 084003 (2015).
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.
The authors declare no competing financial interests.
About this article
Cite this article
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
This article is cited by
Nature Nanotechnology (2023)
Nature Communications (2023)
npj 2D Materials and Applications (2023)
Chinese Journal of Polymer Science (2023)
Scientific Reports (2022)